History.

Újpest FC was founded in 1885. At that time Újpest did not belong to Budapest. Újpest played their first Nemzeti Bajnokság I match in the 1905 Nemzeti Bajnokság I season. In the 1910–11 season they were relegated. Újpest won their first Hungarian league title in the 1929–30 season.  At international level Újpest's most successful period was in the late 1960s and early 1970s. In the 1968–69 Inter-Cities Fairs Cup they were eliminated in the final by Newcastle United. In the 1973–74 European Cup they reached the semi-finals and were eliminated by Bayern München.

Crest and colours.

On 3 July 2017, Újpest FC announced that they changed their crest.

Manufacturers and shirt sponsors.

The following table shows in detail Újpest FC kit manufacturers and shirt sponsors by year: Current sponsorships: Joma, Coca-Cola, Microsoft, Acquaworld Budapest, Ramada Resort Budapest, Puebla ticket, Karzol Trans, Szókép Nyomdaipari Kft., Lamborghini

Stadium.

Újpest's home stadium is Szusza Ferenc Stadion, which has been their home since the opening on 17 September 1922. It was known as Megyeri úti stadium until it was named after the club's legendary player, Ferenc Szusza in October 2003. After the renovations which took place in 2000 and 2001 the ground can hold 13,501 spectators.

Ownership.

On 3 December 2008, it was revealed by BBC Sport that the Premier League club Wolverhampton are considering an alliance with Újpest. Jez Moxey, the Chief executive officer of Wolves said that "We have had some initial discussions in Budapest with the officials of Ujpest. We touched on the issues of loaning players, academies and sharing of best practice on and off the field."  Újpest approached Roland Duchâtelet to become the owner of the club. Although Roland refused the club's offer, he suggested his son to be the proprietor of Újpest. Roland Duchâtelet is the owner of the FC Carl Zeiss Jena and former owner of the Standard Liège, AD Alcorcón and Charlton Athletic F.C.  On 19 October 2011, Roderick Duchâtelet, former director of Germinal Beerschot, bought 95% of the shares of the City Budapest Zrt.  Roderick Duchâtelet said that he indtends to bring back the glory of the 1970s.  On 27 October 2011, Csaba Bartha, managing director of Újpest FC, confirmed that the club received 150 million Hungarian forint from Roderick Duchâtelet.

Supporters.

Supporters of Újpest are mainly from the fourth district of Budapest, the eponymous Újpest. Due to the success in the 1970s, the club gained supporters from all over Budapest and the country.  On May 4, 2007, Újpest were deprived of three points in the 2006–07 Hungarian League season due to racist chanting during their home match against Debrecen. Újpest's official, Szilárd Dányi said "I would ask all of our supporters to think about all factors when they appraise the situation and try to create an atmosphere at matches so that this never happens again. I discussed the topic with the owner and we decided to accept the decision."  Gábor Szerencsi (student at NKE)

Rivalries.

Újpest are in rivalry with several teams from Budapest including Ferencváros, MTK Budapest, Budapest Honvéd and several provincial clubs such as Debrecen and Diósgyőr. Since Újpest have been the third most successful club of the Hungarian Football history by winning 20 Hungarian League titles and 9 Hungarian Cup titles and the most successful Hungarian club in the European football competitions in the 1970s every club in the Hungarian League wants to defeat them. The rivalry with Ferencváros dates back to 1930s when Újpest won their first Hungarian League title. Since then the fixture between the two teams attracts the most spectators in the dometistic league. The matches between the two team often ends in violence which causes big trouble for the Hungarian football. The proposal of personal registration was refused by both clubs.

Újpest Football Club () is a Hungarian professional football club, based in Újpest, Budapest, that competes in Nemzeti Bajnokság I.

乌伊佩斯特足球俱乐部(Újpest Football Club )是匈牙利的一家足球俱乐部。主场设在布达佩斯乌伊佩斯特。俱乐部的代表色是紫色和白色。乌伊佩斯特是匈牙利最为成功的俱乐部之一,获得过20次联赛冠军和8次杯赛冠军。乌伊佩斯特足球俱乐部也是乌伊佩斯特体育俱乐部的成员之一。


Geography.

The Northern Province lies mainly on the great southern African plateau which has been uplifted to an elevation around 1200 metres above sea level. Rift valleys extend clockwise around the province from the north-west to the south. These rift valleys are sometimes outside the borders of the province, as in the case of the Luapula-Mweru valley to the north-west and the Lake Rukwa and Lake Malawi rift valleys to the north east; but the escarpments of the Lake Mweru-wa-Ntipa-Lake Tanganyika rifts in the north, and the Luangwa Valley rift in the east and south-east are just within the province. In places the rift valleys have pushed up highlands: around Kambole and Mbala above Lake Tanganyika, (the Muchinga escarpment above the Luangwa valley, and the highlands along north-eastern border with Tanzania and Malawi which culminate in the Mafinga Hills and Nyika Plateau. These are now in Muchinga Province) These features produce a diverse landscape that varies and poses different challenges, particularly to highway construction, as one moves from one part to another. The Mafinga Hills, which include the highest point in the country at 2301 metres above sea level, once formed a formidable barrier between the Northern and Eastern Provinces that few but the best 4-wheel drive vehicles dared to cross, especially during the rainy season. The shortest road link between the two provinces is now eased by the rehabilitation of the Isoka-Muyombe Road, which traverses their lower slopes.  Rivers, streams and dambos criss-cross the province in profusion, posing yet another great challenge to easy movement of people, goods, and services. The most prominent river on the eastern side is the Luangwa, which has its source in the Mafinga Hills, and which has no road across its valley for a distance of about 800 km. Africa's second longest river, the Congo, has its source in Northern Province via its longest tributary, the Chambeshi River, which rises in the hills south-west of Mbala and divides the province diagonally as it meanders to Lake Bangweulu in the south-west. During times of very heavy rains, these rivers, particularly the Chambeshi and Luangwa, spread across floodplains often several kilometres wide, and create large tracts of both seasonal and permanent lagoons and swamps along their valleys. The Chambeshi feeds the largest wetlands of all, the Bangweulu Wetlands and floodplain in Mpika and Chilubi Districts, known for its Lechwe and birds among other wildlife.  The province also contains three large natural lakes - Lake Bangweulu and its adjacent wetlands (shared with Luapula Province), Lake Mweru-wa-Ntipa in Kaputa District, and the vast Lake Tanganyika in the north, which forms part of Zambia's border with DR Congo and Tanzania.  The above are the national parks and other wildlife areas of Northern Province.

Demographics.

As per the 2010 Zambian census, Northern Province had a population of 1,105,824 accounting to 8.47% of the total Zambian population of 13,092,666. There were 546,851 males and 558,973 females, making the sex ratio to 1,022 for every 1,000 males, compared to the national average of 1,028. The literacy rate stood at 61.00% against a national average of 70.2%. The rural population constituted 81.68%, while the urban population was 18.32%. The total area of the province was 77,650 km and the population density was 14.20 per km. The population density during 2000 Zambian census stood at 14.20. The decadal population growth of the province was 3.20%. The median age in the province at the time of marriage was 20.1. The average household size was 5.0, with the families headed by females being 3.9 and 5.3 for families headed by men. The total eligible voters in the province was 67.40%. The unemployment rate of the province was 6.30%. The total fertility rate was 7.1, complete birth rate was 6.5, crude birth rate was 41.0, child women population at birth was 880, general fertility rate was 182, gross reproduction rate was 2.8 and net reproduction rate was 2.1. The total labour force constituted 60.20% of the total population. Out of the labour force,66.9% were men and 54.1% women. The annual growth rate of labour force was 3.4%. Bemba was the most spoken language with 69.20% speaking it. Albinism is a condition where the victims do not have any pigment in their skin, hair or eyes. The total population in the province with the condition stood at 2,571. The life expectancy at birth stood at 46 compared to the national average of 51.

Languages and Culture.

Northern Province has a number of tribal groups speaking different languages and dialects. However, the language mostly spoken across the province is Icibemba, which is one of the mother tongue of the largest tribal grouping, the Bemba people of Chinsali, Kasama, Mungwi and parts of Mporokoso and Luwingu districts. Other prominent languages include Icinamwanga, spoken by the Namwanga people of Nakonde and Isoka districts, ChiTumbuka, spoken by the Tumbuka people of Lundazi, and Icimambwe, spoken by the Mambwe of Mbala district. Despite its size and the diversity of languages and dialects, the people of Northern Province generally share a common culture.  Each of these tribes has its own traditional leadership headed by either a paramount or senior chief assisted by junior chiefs and village headmen. The most prominent of the chiefs in the province is Chitimukulu, Paramount Chief of the Bemba. Others include Senior Chief Kopa of the Bisa, Senior Chief Muyombe of the Tumbuka, Senior Chieftainess Nawaitwika of the Namwanga, Senior Chief Tafuna of the Lungu and Senior Chief Nsokolo of the Mambwe.

Economy.

Northern Province has no industry at all, and its primary economic activity is agriculture. The most commonly grown crops are maize, millet, sorghum, groundnuts, beans, and rice. Most of the food produced is consumed within the province, though a small percentage is bought by traders for resale along the line of rail.  There are very few farmers who grow crops on a commercial basis in the province. Most of the people are peasant subsistence farmers using the traditional "slash and burn" shifting cultivation locally known as "chitemene", and are barely able to even produce enough to feed themselves. There is also some commercial fishing being done on Lake Tanganyika by established fishing companies in Mpulungu. Most of the fish caught is taken for sale in Lusaka and the Copperbelt on refrigerated trucks. Fishing is also done by small-scale fishermen, who sell their small catches to local traders and others who resell the fish in the nearby towns of Mbala and Kasama.  Mpulungu, 208 km from Kasama, is Zambia's only port, and its harbour is generally used to export bulky goods, such as sugar and cement, to Rwanda and the Democratic Republic of the Congo. In turn, Zambia also imports Kapenta (small, dried fish) and other merchandise from these two countries, as well as Tanzania, through the same port.  The total area of crops planted during the year 2014 in the province was 191,104.56 hectares which constituted 10.07% of the total area cultivated in Zambia. The net production stood at 351,249 metric tonnes, which formed 8.62% of the total agricultural production in the country. Mixed beans was the major crop in the province with 31,898 metric tonnes, constituting 51.66% of the national output.

Communication.

Northern Province has poor communication infrastructure. The telecommunication facilities, which were obsolete until 2005, have somewhat improved with the introduction of cellular phone services in all 12 districts. Prior to this, the situation was so bad that it was easier to make a telephone call outside the province than to any other district within the province as the telephone facilities in these districts were often out of use. However, these cellular phone services are quite costly for government ministries to afford.  The road network is in a poor state. Despite having a total area of 147,826 square kilometers, the province has approximately only 900 kilometers of tarmac, a large portion of which is in dire need of rehabilitation. The rest are gravel roads, the majority of which are in so bad a state that they are almost impassable.

Administration.

Provincial administration is set up purely for administrative purposes. The province is headed by a minister appointed by the President and there are ministries of central government for each province. The administrative head of the province is the Permanent Secretary, appointed by the President. There is a Deputy Permanent Secretary, heads of government departments and civil servants at the provincial level. Northern Province is divided into twelve districts, namely, Chilubi District, Kaputa District, Kasama District, Luwingu District, Mbala District, Mporokoso District, Mpulungu District, Mungwi District, Lupososhi District, Senga Hill District, Lunte District and Nsama District. All the district headquarters are the same as the district names. There are eleven councils in the province, each of which is headed by an elected representative, called councilor. Each councilor holds office for three years. The administrative staff of the council is selected based on Local Government Service Commission from within or outside the district. The office of the provincial government is located in each of the district headquarters and has provincial local government officers and auditors. Each council is responsible for raising and collecting local taxes and the budgets of the council are audited and submitted every year after the annual budget. The elected members of the council do not draw salaries, but are paid allowances from the council. Northern is a predominantly rural district and hence there are no city or municipal councils. The government stipulates 63 different functions for the councils with the majority of them being infrastructure management and local administration. Councils are mandated to maintain each of their community centres, zoos, local parks, drainage system, playgrounds, cemeteries, caravan sites, libraries, museums and art galleries. They also work along with specific government departments for helping in agriculture, conservation of natural resources, postal service, establishing and maintaining hospitals, schools and colleges. The councils prepare schemes that encourage community participation.

Education.

Northern Province has twenty-four high schools. Twenty-one are run by the government, while four are grant-aided (managed by the Catholic Church and the United Church of Zambia with financial support from the government).  All the government high schools run from Grade 10 to 12, while the four managed by the church run from Grade 8 to 12. Six of them are single-sex schools, while the rest admit both girls and boys. There are eight schools that enroll boarding pupils only, while all the others enroll both boarding and day pupils.  As of 2004, the province had 1,208 basic schools, 26 high schools and the number of school children out of school in ages between 7 and 15 stood at 1,208. The unemployment rate was 7 per cent and the general unemployment rate for youth stood at 12 per cent as of 2008. The province had 40 doctors as of 2005. There were 331 Malaria incidence for every 1,000 people in the province as of 2005 and there were 6,958 AIDS death as of 2010.

Northern Province is one of Zambia's ten provinces. It covers approximately one sixth of Zambia in land area. The provincial capital is Kasama. The province is made up of 12 districts, namely Kasama District (the provincial capital), Chilubi District, Kaputa District, Luwingu District, Mbala District, Mporokoso District, Mpulungu District, Mungwi District, Nsama District, Lupososhi District, Lunte District and Senga Hill District. Currently, only Kasama and Mbala have attained municipal council status, while the rest are still district councils. It is widely considered to be the heartland of the Bemba, one of the largest tribes in Zambia.

北方省(英文:Northern Province)是赞比亚9省之一,省内分为12个区,首府卡萨马(Kasama)。该省约占赞比亚五分一的陆地面积,2010年时人口1,304,435人。该省与民主刚果、坦桑尼亚、马拉维接壤


冯诺伊曼-博内斯-哥德尔集合论

Classes in set theory.

The uses of classes.

Classes have several uses in NBG:

Axiom schema versus class existence theorem.

Once classes are added to the language of ZFC, it is easy to transform ZFC into a set theory with classes. First, the axiom schema of class comprehension is added. This axiom schema states: For every formula formula_18 that quantifies only over sets, there exists a class formula_19 consisting of the satisfying the formula—that is, formula_20 Then the axiom schema of replacement is replaced by a single axiom that uses a class. Finally, ZFC's axiom of extensionality is modified to handle classes: If two classes have the same elements, then they are identical. The other axioms of ZFC are not modified.  This theory is not finitely axiomatized. ZFC's replacement schema has been replaced by a single axiom, but the axiom schema of class comprehension has been introduced.  To produce a theory with finitely many axioms, the axiom schema of class comprehension is first replaced with finitely many class existence axioms. Then these axioms are used to prove the class existence theorem which implies every instance of the axiom schema. The proof of this theorem requires only seven class existence axioms, which are used to convert the construction of a formula into the construction of a class satisfying the formula.

Axiomatization of NBG.

Classes and sets.

NBG has two types of objects: classes and sets. Intuitively, every set is also a class. There are two ways to axiomatize this. Bernays used many-sorted logic with two sorts: classes and sets. Gödel avoided sorts by introducing primitive predicates: formula_21 for "formula_19 is a class" and formula_23 for "formula_19 is a set" (in German, "set" is "Menge"). He also introduced axioms stating that every set is a class and that if class formula_19 is a member of a class, then formula_19 is a set. Using predicates is the standard way to eliminate sorts. Elliott Mendelson modified Gödel's approach by having everything be a class and defining the set predicate formula_27 as formula_28 This modification eliminates Gödel's class predicate and his two axioms.  Bernays' two-sorted approach may appear more natural at first, but it creates a more complex theory. In Bernays' theory, every set has two representations: one as a set and the other as a class. Also, there are two membership relations: the first, denoted by "∈", is between two sets; the second, denoted by "η", is between a set and a class. This redundancy is required by many-sorted logic because variables of different sorts range over disjoint subdomains of the domain of discourse.  The differences between these two approaches does not affect what can be proved, but it does affect how statements are written. In Gödel's approach, formula_29 where formula_19 and formula_31 are classes is a valid statement. In Bernays' approach this statement has no meaning. However, if formula_19 is a set, there is an equivalent statement: Define "set formula_33 represents class formula_19" if they have the same sets as members—that is, formula_35 The statement formula_36 where set formula_33 represents class formula_19 is equivalent to Gödel's formula_39  The approach adopted in this article is that of Gödel with Mendelson's modification. This means that NBG is an axiomatic system in first-order predicate logic with equality, and its only primitive notions are class and the membership relation.

Definitions and axioms of extensionality and pairing.

A set is a class that belongs to at least one class: formula_19 is a set if and only if formula_41. A class that is not a set is called a proper class: formula_19 is a proper class if and only if formula_43. Therefore, every class is either a set or a proper class, and no class is both (if the theory is consistent).  Gödel introduced the convention that uppercase variables range over classes, while lowercase variables range over sets. Gödel also used names that begin with an uppercase letter to denote particular classes, including functions and relations defined on the class of all sets. Gödel's convention is used in this article. It allows us to write:  The following axioms and definitions are needed for the proof of the class existence theorem.  Axiom of extensionality. If two classes have the same elements, then they are identical.  This axiom generalizes ZFC's axiom of extensionality to classes.  Axiom of pairing. If formula_49 and formula_50 are sets, then there exists a set formula_51 whose only members are formula_49 and formula_50.  As in ZFC, the axiom of extensionality implies the uniqueness of the set formula_51, which allows us to introduce the notation formula_56  Ordered pairs are defined by: Tuples are defined inductively using ordered pairs:

Class existence axioms and axiom of regularity.

Class existence axioms will be used to prove the class existence theorem: For every formula in formula_60 free set variables that quantifies only over sets, there exists a class of that satisfy it. The following example starts with two classes that are functions and builds a composite function. This example illustrates the techniques that are needed to prove the class existence theorem, which lead to the class existence axioms that are needed.  The class existence axioms are divided into two groups: axioms handling language primitives and axioms handling tuples. There are four axioms in the first group and three axioms in the second group.  Axioms for handling language primitives:  Membership. There exists a class formula_61 containing all the ordered pairs whose first component is a member of the second component.  Intersection (conjunction). For any two classes formula_19 and formula_64, there is a class formula_31 consisting precisely of the sets that belong to both formula_19 and formula_64.  Complement (negation). For any class formula_19, there is a class formula_64 consisting precisely of the sets not belonging to formula_19.  Domain (existential quantifier). For any class formula_19, there is a class formula_64 consisting precisely of the first components of the ordered pairs of formula_19.  By the axiom of extensionality, class formula_31 in the intersection axiom and class formula_64 in the complement and domain axioms are unique. They will be denoted by: formula_79 formula_80 and formula_81 respectively. On the other hand, extensionality is not applicable to formula_61 in the membership axiom since it specifies only those sets in formula_61 that are ordered pairs.  The first three axioms imply the existence of the empty class and the class of all sets: The membership axiom implies the existence of a class formula_84 The intersection and complement axioms imply the existence of formula_85, which is empty. By the axiom of extensionality, this class is unique; it is denoted by formula_86 The complement of formula_87 is the class formula_88 of all sets, which is also unique by extensionality. The set predicate formula_27, which was defined as formula_90, is now redefined as formula_91 to avoid quantifying over classes.  Axioms for handling tuples:  Product by formula_88. For any class formula_19, there is a class formula_64 consisting of the ordered pairs whose first component belongs to formula_19.  Circular permutation. For any class formula_19, there is a class formula_64 whose 3tuples are obtained by applying the circular permutation formula_99 to the 3tuples of formula_19.  Transposition. For any class formula_19, there is a class formula_64 whose 3tuples are obtained by transposing the last two components of the 3tuples of formula_19.  By extensionality, the product by formula_88 axiom implies the existence of a unique class, which is denoted by formula_107 This axiom is used to define the class formula_108 of all : formula_109 and formula_110 If formula_19 is a class, extensionality implies that formula_112 is the unique class consisting of the of formula_113 For example, the membership axiom produces a class formula_61 that may contain elements that are not ordered pairs, while the intersection formula_115 contains only the ordered pairs of formula_61.  The circular permutation and transposition axioms do not imply the existence of unique classes because they specify only the 3tuples of class formula_117 By specifying the 3tuples, these axioms also specify the for formula_118 since: formula_119 The axioms for handling tuples and the domain axiom imply the following lemma, which is used in the proof of the class existence theorem.  Tuple lemma.  Proof:Class formula_124: Apply product by formula_88 to formula_19 to produce formula_127
 Class formula_128: Apply transposition to formula_124 to produce formula_130
 Class formula_131: Apply circular permutation to formula_124 to produce formula_133
 Class formula_134: Apply circular permutation to formula_128, then apply domain to produce formula_136  One more axiom is needed to prove the class existence theorem: the axiom of regularity. Since the existence of the empty class has been proved, the usual statement of this axiom is given.  Axiom of regularity. Every nonempty set has at least one element with which it has no element in common.  This axiom implies that a set cannot belong to itself: Assume that formula_138 and let formula_139 Then formula_140 since formula_141 This contradicts the axiom of regularity because formula_49 is the only element in formula_143 Therefore, formula_144 The axiom of regularity also prohibits infinite descending membership sequences of sets: formula_145  Gödel stated regularity for classes rather than for sets in his 1940 monograph, which was based on lectures given in 1938. In 1939, he proved that regularity for sets implies regularity for classes.

Class existence theorem.

Class existence theorem. Let formula_146 be a formula that quantifies only over sets and contains no free variables other than formula_147 (not necessarily all of these). Then for all formula_148, there exists a unique class formula_19 of such that: formula_150 The class formula_19 is denoted by formula_152  The theorem's proof will be done in two steps:  Transformation rules. In rules 1 and 2 below, formula_157 and formula_158 denote set or class variables. These two rules eliminate all occurrences of class variables before an formula_11 and all occurrences of equality. Each time rule 1 or 2 is applied to a subformula, formula_160 is chosen so that formula_161 differs from the other variables in the current formula. The three rules are repeated until there are no subformulas to which they can be applied. This produces a formula that is built only with formula_154, formula_155, formula_156, formula_11, set variables, and class variables formula_166 where formula_166 does not appear before an formula_11.  Transformation rules: bound variables. Consider the composite function formula of example 1 with its free set variables replaced by formula_177 and formula_178: formula_179 The inductive proof will remove formula_180, which produces the formula formula_181 However, since the class existence theorem is stated for subscripted variables, this formula does not have the form expected by the induction hypothesis. This problem is solved by replacing the variable formula_182 with formula_183 Bound variables within nested quantifiers are handled by increasing the subscript by one for each successive quantifier. This leads to rule 4, which must be applied after the other rules since rules 1 and 2 produce quantified variables.  Proof of the class existence theorem. The proof starts by applying the transformation rules to the given formula to produce a transformed formula. Since this formula is equivalent to the given formula, the proof is completed by proving the class existence theorem for transformed formulas.  Gödel pointed out that the class existence theorem "is a metatheorem, that is, a theorem about the system [NBG], not in the system..." It is a theorem about NBG because it is proved in the metatheory by induction on NBG formulas. Also, its proof—instead of invoking finitely many NBG axioms—inductively describes how to use NBG axioms to construct a class satisfying a given formula. For every formula, this description can be turned into a constructive existence proof that is in NBG. Therefore, this metatheorem can generate the NBG proofs that replace uses of NBG's class existence theorem.  A recursive computer program succinctly captures the construction of a class from a given formula. The definition of this program does not depend on the proof of the class existence theorem. However, this proof is needed to prove that the class constructed by the program satisfies the given formula and is built using the axioms. This program is written in pseudocode that uses a Pascal-style case statement.  formula_184
 formula_185  formula_186
 formula_189  Let formula_153 be the formula of example 2. The function call formula_192 generates the class formula_193 which is compared below with formula_194 This shows that the construction of the class formula_19 mirrors the construction of its defining formula formula_194

Extending the class existence theorem.

Gödel extended the class existence theorem to formulas formula_153 containing relations over classes (such as formula_199 and the unary relation formula_200), special classes (such as formula_9), and operations (such as formula_202 and formula_203). To extend the class existence theorem, the formulas defining relations, special classes, and operations must quantify only over sets. Then formula_153 can be transformed into an equivalent formula satisfying the hypothesis of the class existence theorem.  The following definitions specify how formulas define relations, special classes, and operations:  A is defined by:  The following transformation rules eliminate relations, special classes, and operations. Each time rule 2b, 3b, or 4 is applied to a subformula, formula_160 is chosen so that formula_161 differs from the other variables in the current formula. The rules are repeated until there are no subformulas to which they can be applied. formula_217 and formula_157 denote terms.  Class existence theorem (extended version). Let formula_146 be a formula that quantifies only over sets, contains no free variables other than formula_220, and may contain relations, special classes, and operations defined by formulas that quantify only over sets. Then for all formula_221 there exists a unique class formula_19 of such that formula_150  Proof: Apply the transformation rules to formula_153 to produce an equivalent formula containing no relations, special classes, or operations. This formula satisfies the hypothesis of the class existence theorem. Therefore, for all formula_221 there is a unique class formula_19 of satisfying formula_227

Set axioms.

The axioms of pairing and regularity, which were needed for the proof of the class existence theorem, have been given above. NBG contains four other set axioms. Three of these axioms deal with class operations being applied to sets.  Definition. formula_228 is a function if formula_229  In set theory, the definition of a function does not require specifying the domain or codomain of the function (see Function (set theory)). NBG's definition of function generalizes ZFC's definition from a set of ordered pairs to a class of ordered pairs.  ZFC's definitions of the set operations of image, union, and power set are also generalized to class operations. The image of class formula_19 under the function formula_228 is formula_232 This definition does not require that formula_233 The union of class formula_19 is formula_235 The power class of formula_19 is formula_237 The extended version of the class existence theorem implies the existence of these classes. The axioms of replacement, union, and power set imply that when these operations are applied to sets, they produce sets.  Axiom of replacement. If formula_228 is a function and formula_33 is a set, then formula_240, the image of formula_33 under formula_228, is a set.  Not having the requirement formula_244 in the definition of formula_245 produces a stronger axiom of replacement, which is used in the following proof. Theorem (NBG's axiom of separation). If formula_19 is a set and formula_64 is a subclass of formula_193 then formula_64 is a set.
 Proof: The class existence theorem constructs the restriction of the identity function to formula_64: formula_251 Since the image of formula_19 under formula_253 is formula_64, the axiom of replacement implies that formula_64 is a set. This proof depends on the definition of image not having the requirement formula_244 since formula_257 rather than formula_258  Axiom of union. If formula_33 is a set, then there is a set containing formula_260  Axiom of power set. If formula_33 is a set, then there is a set containing formula_263  Theorem. If formula_33 is a set, then formula_266 and formula_267 are sets.
 Proof: The axiom of union states that formula_266 is a subclass of a set formula_269, so the axiom of separation implies formula_266 is a set. Likewise, the axiom of power set states that formula_267 is a subclass of a set formula_269, so the axiom of separation implies that formula_267 is a set.  Axiom of infinity. There exists a nonempty set formula_33 such that for all formula_49 in formula_33, there exists a formula_50 in formula_33 such that formula_49 is a proper subset of formula_50.  The axioms of infinity and replacement prove the existence of the empty set. In the discussion of the class existence axioms, the existence of the empty class formula_87 was proved. We now prove that formula_87 is a set. Let function formula_284 and let formula_33 be the set given by the axiom of infinity. By replacement, the image of formula_33 under formula_228, which equals formula_87, is a set.  NBG's axiom of infinity is implied by ZFC's axiom of infinity: formula_289 The first conjunct of ZFC's axiom, formula_290, implies the first conjunct of NBG's axiom. The second conjunct of ZFC's axiom, formula_291, implies the second conjunct of NBG's axiom since formula_292 To prove ZFC's axiom of infinity from NBG's axiom of infinity requires some of the other NBG axioms (see Weak axiom of infinity).

Axiom of global choice.

The class concept allows NBG to have a stronger axiom of choice than ZFC. A choice function is a function formula_5 defined on a set formula_4 of nonempty sets such that formula_7 for all formula_8 ZFC's axiom of choice states that there exists a choice function for every set of nonempty sets. A global choice function is a function formula_1 defined on the class of all nonempty sets such that formula_2 for every nonempty set formula_3 The axiom of global choice states that there exists a global choice function. This axiom implies ZFC's axiom of choice since for every set formula_4 of nonempty sets, formula_301 (the restriction of formula_1 to formula_4) is a choice function for formula_304 In 1964, William B. Easton proved that global choice is stronger than the axiom of choice by using forcing to construct a model that satisfies the axiom of choice and all the axioms of NBG except the axiom of global choice. The axiom of global choice is equivalent to every class having a well-ordering, while ZFC's axiom of choice is equivalent to every set having a well-ordering.  Axiom of global choice. There exists a function that chooses an element from every nonempty set.

History.

Von Neumann's 1925 axiom system.

Von Neumann published an introductory article on his axiom system in 1925. In 1928, he provided a detailed treatment of his system. Von Neumann based his axiom system on two domains of primitive objects: functions and arguments. These domains overlap—objects that are in both domains are called argument-functions. Functions correspond to classes in NBG, and argument-functions correspond to sets. Von Neumann's primitive operation is function application, denoted by ["a", "x"] rather than "a"("x") where "a" is a function and "x" is an argument. This operation produces an argument. Von Neumann defined classes and sets using functions and argument-functions that take only two values, "A" and "B". He defined "x" ∈ "a" if ["a", "x"] ≠ "A".  Von Neumann's work in set theory was influenced by Georg Cantor's articles, Ernst Zermelo's 1908 axioms for set theory, and the 1922 critiques of Zermelo's set theory that were given independently by Abraham Fraenkel and Thoralf Skolem. Both Fraenkel and Skolem pointed out that Zermelo's axioms cannot prove the existence of the set {"Z", "Z", "Z",...} where "Z" is the set of natural numbers and "Z" is the power set of "Z". They then introduced the axiom of replacement, which would guarantee the existence of such sets. However, they were reluctant to adopt this axiom: Fraenkel stated "that Replacement was too strong an axiom for 'general set theory'", while "Skolem only wrote that 'we could introduce' Replacement".  Von Neumann worked on the problems of Zermelo set theory and provided solutions for some of them:

Von Neumann's 1929 axiom system.

In 1929, von Neumann published an article containing the axioms that would lead to NBG. This article was motivated by his concern about the consistency of the axiom of limitation of size. He stated that this axiom "does a lot, actually too much." Besides implying the axioms of separation and replacement, and the well-ordering theorem, it also implies that any class whose cardinality is less than that of "V" is a set. Von Neumann thought that this last implication went beyond Cantorian set theory and concluded: "We must therefore discuss whether its [the axiom's] consistency is not even more problematic than an axiomatization of set theory that does not go beyond the necessary Cantorian framework."  Von Neumann started his consistency investigation by introducing his 1929 axiom system, which contains all the axioms of his 1925 axiom system except the axiom of limitation of size. He replaced this axiom with two of its consequences, the axiom of replacement and a choice axiom. Von Neumann's choice axiom states: "Every relation "R" has a subclass that is a function with the same domain as "R"."  Let "S" be von Neumann's 1929 axiom system. Von Neumann introduced the axiom system "S" + Regularity (which consists of "S" and the axiom of regularity) to demonstrate that his 1925 system is consistent relative to "S". He proved: These results imply: If "S" is consistent, then von Neumann's 1925 axiom system is consistent. Proof: If "S" is consistent, then "S" + Regularity is consistent (result 1). Using proof by contradiction, assume that the 1925 axiom system is inconsistent, or equivalently: the 1925 axiom system implies a contradiction. Since "S" + Regularity implies the axioms of the 1925 system (result 2), "S" + Regularity also implies a contradiction. However, this contradicts the consistency of "S" + Regularity. Therefore, if "S" is consistent, then von Neumann's 1925 axiom system is consistent.  Since "S" is his 1929 axiom system, von Neumann's 1925 axiom system is consistent relative to his 1929 axiom system, which is closer to Cantorian set theory. The major differences between Cantorian set theory and the 1929 axiom system are classes and von Neumann's choice axiom. The axiom system "S" + Regularity was modified by Bernays and Gödel to produce the equivalent NBG axiom system.

Bernays' axiom system.

In 1929, Paul Bernays started modifying von Neumann's new axiom system by taking classes and sets as primitives. He published his work in a series of articles appearing from 1937 to 1954. Bernays stated that:  Bernays handled sets and classes in a two-sorted logic and introduced two membership primitives: one for membership in sets and one for membership in classes. With these primitives, he rewrote and simplified von Neumann's 1929 axioms. Bernays also included the axiom of regularity in his axiom system.

Gödel's axiom system (NBG).

In 1931, Bernays sent a letter containing his set theory to Kurt Gödel. Gödel simplified Bernays' theory by making every set a class, which allowed him to use just one sort and one membership primitive. He also weakened some of Bernays' axioms and replaced von Neumann's choice axiom with the equivalent axiom of global choice. Gödel used his axioms in his 1940 monograph on the relative consistency of global choice and the generalized continuum hypothesis.  Several reasons have been given for Gödel choosing NBG for his monograph:  Gödel's achievement together with the details of his presentation led to the prominence that NBG would enjoy for the next two decades. In 1963, Paul Cohen proved his independence proofs for ZF with the help of some tools that Gödel had developed for his relative consistency proofs for NBG. Later, ZFC became more popular than NBG. This was caused by several factors, including the extra work required to handle forcing in NBG, Cohen's 1966 presentation of forcing, which used ZF, and the proof that NBG is a conservative extension of ZFC.

NBG, ZFC, and MK.

NBG is not logically equivalent to ZFC because its language is more expressive: it can make statements about classes, which cannot be made in ZFC. However, NBG and ZFC imply the same statements about sets. Therefore, NBG is a conservative extension of ZFC. NBG implies theorems that ZFC does not imply, but since NBG is a conservative extension, these theorems must involve proper classes. For example, NBG implies that the proper class "V" can be well-ordered and that every proper class can be put into one-to-one correspondence with "V".  One consequence of conservative extension is that ZFC and NBG are equiconsistent. Proving this uses the principle of explosion: from a contradiction, everything is provable. Assume that either ZFC or NBG is inconsistent. Then the inconsistent theory implies the contradictory statements ∅ = ∅ and ∅ ≠ ∅, which are statements about sets. By the conservative extension property, the other theory also implies these statements. Therefore, it is also inconsistent. So although NBG is more expressive, it is equiconsistent with ZFC. This result together with von Neumann's 1929 relative consistency proof implies that his 1925 axiom system with the axiom of limitation of size is equiconsistent with ZFC. This completely resolves von Neumann's concern about the relative consistency of this powerful axiom since ZFC is within the Cantorian framework.  Even though NBG is a conservative extension of ZFC, a theorem may have a shorter and more elegant proof in NBG than in ZFC (or vice versa). For a survey of known results of this nature, see.  Morse–Kelley set theory has an axiom schema of class comprehension that includes formulas whose quantifiers range over classes. MK is a stronger theory than NBG because MK proves the consistency of NBG, while Gödel's second incompleteness theorem implies that NBG cannot prove the consistency of NBG.  For a discussion of some ontological and other philosophical issues posed by NBG, especially when contrasted with ZFC and MK, see Appendix C of.

Models.

ZFC, NBG, and MK have models describable in terms of the cumulative hierarchy "V" and the constructible hierarchy "L". Let "V" include an inaccessible cardinal κ, let "X" ⊆ "V", and let Def("X") denote the class of first-order definable subsets of "X" with parameters. In symbols where "formula_306" denotes the model with domain formula_307 and relation formula_11, and "formula_309" denotes the satisfaction relation:  Then:

Category theory.

The ontology of NBG provides scaffolding for speaking about "large objects" without risking paradox. For instance, in some developments of category theory, a "large category" is defined as one whose objects and morphisms make up a proper class. On the other hand, a "small category" is one whose objects and morphisms are members of a set. Thus, we can speak of the "category of all sets" or "category of all small categories" without risking paradox since NBG supports large categories.  However, NBG does not support a "category of all categories" since large categories would be members of it and NBG does not allow proper classes to be members of anything. An ontological extension that enables us to talk formally about such a "category" is the conglomerate, which is a collection of classes. Then the "category of all categories" is defined by its objects: the conglomerate of all categories; and its morphisms: the conglomerate of all morphisms from "A" to "B" where "A" and "B" are objects. On whether an ontology including classes as well as sets is adequate for category theory, see.

In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel-Choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets. NBG can define classes that are larger than sets, such as the class of all sets and the class of all ordinals. Morse–Kelley set theory (MK) allows classes to be defined by formulas whose quantifiers range over classes. NBG is finitely axiomatizable, while ZFC and MK are not.

在数学基础中,冯·诺伊曼-博内斯-哥德尔集合论(英语:von Neumann–Bernays–Gödel Set Theory,英语:NBG)是设计生成同Zermelo-Fraenkel 集合论与选择公理一起(ZFC)同样结果的集合论公理系统,但只有有限数目的公理,即是不使用公理模式。


Location.

San Francisco's gay village is mostly concentrated in the business district that is located on Castro Street from Market Street to 19th Street. It extends down Market Street toward Church Street and on both sides of the Castro neighborhood from Church Street to Eureka Street. Although the greater gay community was, and is, concentrated in the Castro, many gay people live in the surrounding residential areas bordered by Corona Heights, the Mission District, Noe Valley, Twin Peaks, and Haight-Ashbury neighborhoods. Some consider it to include Duboce Triangle and Dolores Heights, which both have a strong LGBT presence.  Castro Street, which originates a few blocks north at the intersection of Divisadero and Waller Streets, runs south through Noe Valley, crossing the 24th Street business district and ending as a continuous street a few blocks farther south as it moves toward the Glen Park neighborhood. It reappears in several discontinuous sections before ultimately terminating at Chenery Street, in the heart of Glen Park.

History.

Castro Street was named after José Castro (1808–1860), a Californian leader of Mexican opposition to U.S. rule in California in the 19th century, and alcalde of Alta California from 1835 to 1836. The neighborhood known as the Castro, in the district of Eureka Valley, was created in 1887 when the Market Street Railway Company built a line linking Eureka Valley to downtown.  In 1891, Alfred E. Clarke built his mansion at the corner of Douglass and Caselli Avenue at 250 Douglass which is commonly referenced as the Caselli Mansion. It survived the 1906 earthquake and fire which destroyed a large portion of San Francisco.

Early years.

Up to the 19th century, the areal possession of the Russian Empire in North America included the modern-day U.S. state of Alaska and settlements in the modern-day U.S. states of California (1 settlement) and Hawaii (3 settlements, starting in 1817). These Russian possessions were collectively and officially referred to by the name Russian America from 1733 to 1867. Formal incorporation of the possessions by Russia did not take place until the establishment of the Russian-American Company (RAC) in 1799.  In 1809–1917, Finland was an autonomous part of the Russian Empire and was officially referred to as the Grand Duchy of Finland. During this era, the operations of both merchant and naval fleets as well as construction of naval vessels, relied heavily on Finnish know-how, seamen and officers. At the time, Russia was a relatively young naval power, gaining gradually access to the Baltic Sea only after the city of Saint Petersburg was founded on its coast in 1703, becoming officially part of Russia only at the end of the Great Northern War (1700–1721) in 1721.  In 1839, Sitka Lutheran Church, the first Protestant congregation on the west coast of the Americas and the first Lutheran congregation on the entire Pacific Rim was founded in Sitka, Alaska, by Finns who worked for the Russian-American Company. From the start, in 1840–1865, three consecutive Finnish pastors served this pastorate: Uno Cygnaeus (1840–1845), Gabriel Plathan (1845–1852) and Georg Gustaf Winter (1852–1865). The Finns Aaron Sjöstrom and Otto Reinhold Rehn served as the parish organists/sextons during this period.  In 1841, under the governorship of Russian America by Finnish Arvid Adolf Etholén (1840–1845) (promoted to rear admiral in 1847), the Russian-American area of Fort Ross in Bodega Bay, California, was sold to Johann Sutter. On January 24, 1848, the first California gold was discovered on Sutter's land in Coloma, California, leading to the California Gold Rush, after news of this were spread abroad, mainly by the Finnish seamen in the service of the Russian-American Company.  During the final three decades of the existence of Russian America, Finnish Chief Managers ("governors") of Russian America included Arvid Adolf Etholén (a.k.a. Etolin) in 1840–1845 and Johan Hampus Furuhjelm in 1859–1864. A third Finn, Johan Joachim von Bartram, declined the offer for the five-year term between 1850 and 1855. All three were high ranking Imperial naval officers. In reference to San Francisco, researcher Maria J. Enckell states the following about the Finns in the Russian-American Company:  Russia relied heavily on Finnish seamen. These seamen manned Russian naval ships as well as its deep-sea-going vessels. Company records show that in the early 1800s these ships were crewed predominantly by merchant seamen from Finland. From 1840 onward the Company's around-the-world ships were manned entirely by Finnish merchant skippers and crews. Most Company ships stationed in Sitka and the Northern Pacific were likewise manned by Finnish skippers and Finnish crews.  <poem>... Significant too is that from the early 1800s the Finnish seamen sailing these ships had journeyed up and down the North and South American coasts. Salt, used by the Company in preserving pelts, was obtained on islands in Baja California. Fort Ross in Bodega Bay, just north of San Francisco, was a stop on that route until 1841 when the fort was sold to the "swindler" Johann Sutter, on whose land the first California Gold was found. Thus, all Finnish seamen plying these waters knew every nook and cranny on these shores. Similarly they knew equally well the coast on the Asiatic side. Returning to Finland on their mandatory around-the-world journeys, they spread the news of the riches they had seen.  San Francisco's harbor records and the Russian Consular records display the names of many Finnish and Baltic Russian Alaska skippers busily plying the waters between San Francisco, Petropavlovsk, Nikolajefsk and Vladivostok... Long before the turn of the century 11% of San Francisco's seaman community were Finns. The commercial activities of these former Finnish Russian-American Company skippers and their men were impressive. At least two are known to have become multimillionaires: Gustaf Nybom (later Niebaum), the founder of Inglenook wineries, and Otto Wilhelm Lindholm of Vladivostok. Their business ventures had interests spread across the Northern Pacific. This activity continued until 1922 and the Soviet terror, when Vladivostok's numerous Finns and Manchurians were rounded up, marched to the central square and shot.</poem>

Late 19th century.

During the California Gold Rush and in its aftermath, a substantial Finnish population had settled in San Francisco. In addition to Etholén, Furuhjelm and Niebaum, a number of Finns had become household names in the social circles of San Francisco by the time when the Finnish corvette Kalevala anchored in San Francisco on November 14, 1861. Accordingly, Kalevala's visit in the city received a very warm welcome and created much attention. In 1863, a six-vessel Russian Imperial Navy squadron, a part of the Russian Pacific Fleet, sailed via Vladivostok to the West Coast of the United States, to help defend the waters there against a possible attack by the United Kingdom or France, during the American Civil War (April 12, 1861 – May 10, 1865). In addition to the Finnish-built corvette "Kalevala" now returning to the U.S. West Coast, this squadron included three other corvettes, "Bogatyr", "Rynda" and "Novik" (Russian: "Новик"), as well as two Finnish-built clippers, the sister-ships "Abrek" (Russian: "Абрек") and "Vsadnik" (Russian: "Всадник"), both built in the southwestern Finnish town of Pori and launched in 1860. Finnish officers serving in the squadron included "Theodor Kristian Avellan", who later became the Minister of Naval Affairs of the Russian Empire (similar role to Great Britain's First Lord of the Admiralty). Among Finnish officers participating in the expedition were also Mr. "Enqvist" and Mr. "Etholén" (not Governor Etholén of Russian America).  At the time when Finnish Sea Captain Gustave Niebaum, the founder of Inglenook Winery (1879) in Rutherford, California, was busy conducting business in the San Francisco Bay Area and Alaska – from the late 19th to the early 20th century –, both places had considerably large Finnish settlements. As the Governor of Russian America from 1858 to 1864, Finnish Johan Hampus Furuhjelm helped pave way for the American Alaska purchase, just like Gustave Niebaum did as the Consul of Russia for the United States in San Francisco in 1867 (at the time Finland was an autonomous Grand Duchy of Russia), when Alaska became part of the United States of America.  During his governorship of Russian America, Furuhjelm put an end to the hostilities involving groups of the native peoples of Alaska, and he succeeded in abolishing the Alaskan "Ice Treaty" with San Francisco. According to a contract which had been signed, Russian America had to deliver a certain amount of ice to San Francisco at a fixed price. The problem was that the product melted down on the way to the warmer climates. The ice contract became very awkward for the Russian colony. Furuhjelm arranged for a new contract to sell ice to San Francisco: 3,000 tons at $25.00 a ton.  Officially registered Finnish Club No. 1 was established in the Castro District of San Francisco in 1882. Soon after, two "Finnish Halls" were erected nearby. One was located at the corner of 24th Street and Hoffman Street. The other hall was located on Flint Street, on the "Rocky Hill" above Castro, an area densely populated by Finns at the time, consequently nicknamed "Finn Town".  In 1899, the First Finnish Lutheran Church was founded on 50 Belcher Street, in what then was considered part of the "Eureka Valley" district of San Francisco, but what is located on the outskirts of what today is best known as the Castro District. Next to it, on September 17, 1905, the cornerstone was laid for the Danish St. Ansgar Church at 152 Church Street, between Market Street and Duboce Avenue. During the April 18, 1906, San Francisco earthquake and its aftermath, the parsonage served as a feeding station and hospital. In 1964, St. Ansgar merged with First Finnish Lutheran Church. The name for the united church, St. Francis Lutheran Church, was derived from San Francisco.  Before the 1906 San Francisco earthquake, nearly all the kids attending the McKinley school (now McKinley Elementary School) at 1025 14th Street (at Castro) were Finnish. Following the earthquake, a large number of Finns from San Francisco and elsewhere moved to Berkeley, where a Finnish community had been established already before the earthquake. A large part of the early Berkeley population was Finnish. The brick and wood frame of the St. Francis Lutheran Church building survived the 1906 San Francisco earthquake and then was used for several months as an infirmary. Following the earthquake, the same year, Finns founded the "Lutheran Church of the Cross" in Berkeley, at University Avenue, where the Lutheran congregation still operates today.  In c. 1910, a bathhouse called Finnila's Finnish Baths began serving customers in the Castro District, at 9 Douglass Street. Its opening as an official business serving the general public took place in 1913. In 1919, the business moved to 4032 17th Street, a half block west from the busy Castro Street. In 1932, the business moved again, now to 2284 Market Street. In 1986, after having been stationed in the Castro District for over seven decades, the business moved the final time, now to 465 Taraval Street in the San Francisco's Sunset District, where it continued as Finnila's Health Club, serving women only. Despite public outcry and attempts to prevent the closing of the popular Finnila's Market Street bathhouse, the old bathhouse building was demolished by Alfred Finnila soon after the farewell party held in the end of December 1985. Today, the Finnila family owns the new "Market & Noe Center" building at the location of the old bathhouse, in the corner of Market and Noe Streets.

Change of character.

From 1910 on, the Castro District of San Francisco and some of the surrounding areas was known by the term "Little Scandinavia", because of the large number of the residents in the area originating from Finnish, Danish, Norwegian and Swedish ancestry.  The 1943 novel "Mama's Bank Account" by Kathryn Forbes focused on a Norwegian family living in the area in the 1910s. Forbes' book served as the inspiration for John Van Druten's 1944 play "I Remember Mama". The play was adapted to a Broadway theater production in 1944; to a movie in 1948; to a CBS Mama television series running from 1949 until 1957; to a "Lux Radio Theater" play in the late 1950s; and to a Broadway musical in 1979. "Mama's Bank Account" reflected a (then) Eureka Valley neighborhood, where for generations Norwegians worshiped at the Norwegian Lutheran Church at 19th and Dolores streets, and met for fraternal, social events, and Saturday night dances at Dovre Hall, 3543 18th Street, now the Women's Building.  The Cove on Castro used to be called The Norse Cove at the time. The Scandinavian Seamen's Mission operated for a long time on 15th Street, off Market Street, just around the corner from the Swedish-American Hall, which remains in the district. In the 1920s – during prohibition – the downstairs of the Swedish-American Hall served as a speak-easy, one of many in the area. "Unlicensed saloons" were known as "speak-easies", according to an 1889 newspaper. They were "so called because of the practice of speaking quietly about such a place in public, or when inside it, so as not to alert the police or neighbors".  Scandinavian-style "half-timber" construction can still be seen in some of the buildings along Market Street, between Castro and Church Streets. A restaurant called Scandinavian Deli operated for decades on Market Street, between Noe and Sanchez Streets, almost directly across the street from Finnila's.  Receiving an influx of Irish, Italian and other immigrants in the 1930s, the Castro gradually became an ethnically mixed working-class neighborhood, and it remained so until the mid-1960s. There was originally a cable car line with large double-ended cable cars that ran along Castro Street from Market Street to 29th St., until the tracks were dismantled in 1941 and the cable car line was replaced by the 24 MUNI bus. The Castro is at the end of the straight portion of the Market Street thoroughfare, and a mostly residential area follows Market Street as it curves and rises up and around the Twin Peaks mountains.

LGBT community.

The U.S. military discharged thousands of gay servicemen from the Pacific theatre in San Francisco during World War II (early 1940s) because of their sexuality. Many settled in the Bay Area, San Francisco and Sausalito. In San Francisco, an established gay community had begun in numerous areas including Polk Street (which used to be regarded as the city's gay center from the 1950s to the early 1980s), the Tenderloin and South of Market. The 1950s saw large numbers of families moving out of the Castro to the suburbs in what became known as the "White flight", leaving open large amounts of real estate and creating attractive locations for gay purchasers. By 1963, the Castro's first gay bar was opened called the "Missouri Mule".  The Castro's age as a gay mecca began during the late 1960s with the Summer of Love in the neighbouring Haight-Ashbury district in 1967. The two neighbourhoods are separated by a large mountain, topped by Buena Vista Park. The hippie and free love movements had fostered communal living and free society ideas including the housing of large groups of people in hippie communes. Androgyny became popular with men even in full beards as gay hippie men began to move into the area. The 1967 gathering brought tens of thousands of middle-class youth from all over the United States to the Haight which saw its own exodus when well-organized individuals and collectives started to see the Castro as an oasis from the massive influx. Many of the hippies had no way to support themselves or places to shelter. The Haight became drug-ridden and violent, chasing off the gay population, who looked for a more stable area to live.  The gay community created an upscale, fashionable urban center in the Castro District in the 1970s. Many San Francisco gays also moved there in the years around 1970 from what was then the most prominent gay neighborhood, Polk Gulch, because large Victorian houses were available at low rents or available for purchase for low down payments when their former middle-class owners had fled to the suburbs.  By 1973, Harvey Milk, who would become the most famous resident of the neighborhood, opened a camera store, Castro Camera, and began political involvement as a gay activist, further contributing to the notion of the Castro as a gay destination. Some of the culture of the late 1970s included what was termed the "Castro clone", a mode of dress and personal grooming that exemplified butchness and masculinity of the working-class men in construction—tight denim jeans, black or sand combat boots, tight T-shirt or, often, an Izod crocodile shirt, possibly a red plaid flannel outer shirt, and usually sporting a mustache or full beard—in vogue with the gay male population at the time, and which gave rise to the nickname "Clone Canyon" for the stretch of Castro Street between 18th and Market Streets.  There were numerous famous watering holes in the area contributing to the nightlife, including the Corner Grocery Bar, Toad Hall, the Pendulum, the Midnight Sun, Twin Peaks, and the Elephant Walk. A typical daytime street scene of the period is perhaps best illustrated by mentioning the male belly dancers who could be found holding forth in good weather at the corner of 18th and Castro on "Hibernia Beach", in front of the financial institution from which it drew its name. Then at night, after the bars closed at 2 AM, the men remaining at that hour often would line up along the sidewalk of 18th Street to indicate that they were still available to go home with someone (aka The Meat Rack).  The area was heavily impacted by the HIV/AIDS crisis of the 1980s. Beginning in 1984, city officials began a crackdown on bathhouses and launched initiatives that aimed to prevent the spread of AIDS. Kiosks lining Market Street and Castro Street now have posters promoting safe sex and testing right alongside those advertising online dating services.  In 2019, San Francisco Board of Supervisors member Rafael Mandelman authored an ordinance to create the Castro LGBTQ Cultural District; the ordinance was passed unanimously.

Attractions.

One of the more notable features of the neighborhood is Castro Theatre, a movie palace built in 1922 and one of San Francisco's premier movie houses.  18th and Castro is a major intersection in the Castro, where many historic events, marches, and protests have taken and continue to take place.  A major cultural destination in the neighborhood is the GLBT History Museum, which opened for previews on Dec. 10, 2010, at 4127 18th St. The grand opening of the museum took place on the evening of Jan. 13, 2011. The first full-scale, stand-alone museum of lesbian, gay, bisexual and transgender history in the United States (and only the second in the world after the Schwules Museum in Berlin), the GLBT History Museum is a project of the GLBT Historical Society.  The F Market heritage streetcar line turnaround at Market and 17th-streets where the Jane Warner city park let sits. Across Castro street is the Harvey Milk Plaza in honor of its most famous resident with its iconic giant flag pole with an oversized rainbow flag, symbol of the LGBT community. Below street level is the main entrance to the Castro Street Station, a Muni Metro subway station and a multitiered park. Milk's camera store and campaign headquarters which were at 575 Castro has a memorial plaque and mural on the inside of the store, now housing the Human Rights Campaign Action Center and Store. There is a smaller mural above the sidewalk on the building showing Milk looking down on the street fondly.  Across Market Street from Harvey Milk Plaza, and slightly up the hill, is the Pink Triangle Park – 17th Street at Market, a city park and monument named after the pink triangles forcibly worn by gay prisoners persecuted by the Nazis during World War II.  Harvey's was formerly the Elephant Walk, raided by police after the White Night Riots.  The Hot Cookie Bakery located on Castro Street is a world-famous destination serving cookies. It is especially known for its coconut macaroons.  Twin Peaks is the first gay bar in the city, and possibly the United States, with plate glass windows to fully visibly expose patrons to the public is located at the intersection of Market and Castro.  The Hartford Street Zen Center is also located in the Castro, as well as the Most Holy Redeemer Catholic Church, 100 Diamond Street.  Special events, parade and street fairs that are held in the Castro include the Castro Street Fair, the Dyke March, the famed Halloween in the Castro which was discontinued in 2007 due to street violence, Pink Saturday discontinued in the Castro in 2016, and the San Francisco International LGBT Film Festival.  A LGBTQ Walk of Fame, the Rainbow Honor Walk, was installed in August 2014 with an inaugural twenty sidewalk bronze plaques representing past LGBTQ icons in their field, who continue to serve as inspirations. The walk is originally planned to coincide with the business district of the Castro and eventually include 500 bronze plaques.  The main business section of Castro St from Market to 19th street were under reconstruction and repaving in 2014 to address a number of neighborhood concerns. The area has heavy vehicular traffic as well as many visitors. As part of the work the sidewalks were widened and new trees were planted. Additionally 20 historical cement etchings covering from the inception to the area being settled to the 2010s sweeping gay marriage movement victories were installed in September 2014.

Castro Street History Walk.

A separate sidewalk installation, the Castro Street History Walk (CSHW), is a series of twenty historical fact plaques about the neighborhood—ten from pre-1776 to the 1960s before the Castro became known as a gay neighborhood, and ten “significant events associated with the queer community in the Castro”—contained within the 400 and 500 blocks of the street between 19th and Market streets. They were installed at the same time as the inaugural twenty RHW plaques. The CSHW goes in chronological order starting at Harvey Milk Plaza at Market Street, up to 19th Street, and returning on the opposite side of Castro Street. The $10,000 CSHW was paid for by the Castro Business District (CBD) which “convened a group of local residents and historians to work with Nicholas Perry, a planner and urban designer at the San Francisco Planning Department who worked on the sidewalk-widening project and lives in the Castro” to develop the facts. Each fact was required to be about the neighborhood or the surrounding Eureka Valley. The facts are limited to 230 characters, and were installed in pairs along with a single graphic reminiscent of the historic Castro Theater.

LGBT tourism.

San Francisco has a large and thriving tourist economy due to ethnic and cultural communities such as Chinatown, North Beach, Haight-Ashbury and the Castro. The Castro is a site of economic success that brings in capital all year round with many events catered to the gay community along with everyday business.  The Castro is a "thriving marketplace for all things gay" meaning everything in the area is catered to people who identify with LGBT culture and other associated meanings to the word gay. There are cafes, the Castro Theater, and many businesses that cater to or openly welcome LGBT consumers. These establishments make the Castro an area of high spending and lead to high tourist traffic. In addition to the city's locals, people travel to visit the shops and restaurants as well as the events that take place, such as the Castro Street Fair. Events such as the fairs drum up business for the community and bring in people from all over the nation who visit solely for the atmosphere the Castro provides. People who do not necessarily feel comfortable expressing themselves in their own community have the freedom to travel to places such as the Castro to escape the alienation and feel accepted. There is a sense of belonging and acceptance that is promoted throughout the district to accommodate non-heteronormative people that many LGBT travellers are attracted to.  The Golden Gate Business Association (GGBA) was created in 1974 to help promote the Castro as a place for tourists, but also San Francisco and LGBT businesses as a whole. The GGBA sought to gain local political power and hoped to achieve their gains through an increase in gay tourism. This association formed the San Francisco Gay Tourism and Visitor's Bureau in 1983. Politically, the Bureau was neoliberal and focused on economic interests while denying poverty and prejudice. The LGBT tourism industry drives and benefits the economy due to the constant influx of consumers.

The Castro District, commonly referred to as the Castro, is a neighborhood in Eureka Valley in San Francisco. The Castro was one of the first gay neighborhoods in the United States. Having transformed from a working-class neighborhood through the 1960s and 1970s, the Castro remains one of the most prominent symbols of lesbian, gay, bisexual, and transgender (LGBT) activism and events in the world.

卡斯特罗街(Castro Street),一般在英文常被称做「The Castro」,是位于加州旧金山市的一个区,邻近欧瑞卡谷区(),是世界著名的同志村和观光景点。


Early life.

Born in Edinburgh, Scotland, he studied at University of Edinburgh and later Magdalen College, Oxford.  In 1898, he entered into colonial service and worked in Hong Kong. After initial service in Hong Kong, Johnston was transferred to the British leased territory at Weihaiwei in 1906 on the coast of the Shandong Peninsula as a District Officer, working with Sir James Haldane Stewart Lockhart. Johnston was a keen traveller, in 1902 exploring Tonkin, Laos and Siam. In 1904 he visited Kiautschou, Jinan and later Korea. In January 1906, he undertook a year-long journey from Peking to Mandalay, publishing an account of his experiences in 1908.

Tutor to Puyi, in the Forbidden City.

In 1919, he was appointed tutor of thirteen-year-old Puyi who still lived inside the Forbidden City in Beijing as a non-sovereign monarch.  As the Scottish-born tutor to the Dragon Emperor, Johnston and Isabel Ingram, daughter of an American missionary and the empress's tutor, were the only foreigners in history to be allowed inside the inner court of the Qing Dynasty. Johnston carried high imperial titles and lived in both the Forbidden City and the New Summer Palace.  Johnston met the Ming dynasty Imperial descendant, the Marquis of Extended Grace Zhu Yuxun and arranged for him to meet Puyi in the Forbidden City.  After Puyi was expelled from the Forbidden City in 1924, Johnston served as Secretary to the British China Indemnity Commission (1926). In 1927, he was appointed the second civilian Commissioner at Weihaiwei. He ran the territory until it was returned to the Republic of China on 1 October 1930.

After China.

Johnston was appointed Professor of Chinese in the University of London in 1931, a post based at the School of Oriental and African Studies, to which he bequeathed his library in 1935. This library, one of the finest collections of Chinese and East Asian books in the country, consists of over 16,000 volumes. He was not a natural teacher, and hated university administration.  He retained his ties with Puyi, which proved an embarrassment after the former emperor assumed the throne of the Japanese puppet state of Manchukuo.  Johnston retired in 1937, having acquired the small island of Eilean Righ in Loch Craignish, Scotland, on which he created for himself a Chinese Garden and flew the flag of Manchukuo. After a short illness, he died in Edinburgh. In his will, he requested that no religious ceremony be conducted. In accordance with his wishes, he was cremated. His ashes were scattered on the island of Eilean Righ and surrounding Loch.  He never married but was at one stage engaged to the historian Eileen Power, and was close to author Stella Benson.  Mrs Elizabeth Sparshott, to whom he was engaged at the time leading up to his death, burned many of his letters and other materials, at Johnston's request.  Johnston's book "Twilight in the Forbidden City" (1934) describes his experiences in Beijing and was used as a source for Bernardo Bertolucci's film dramatization of Puyi's life "The Last Emperor". He was portrayed by Peter O'Toole in the film.

Sir Reginald Fleming Johnston, (13 October 1874 – 6 March 1938) was a Scottish diplomat who served as the tutor and advisor to Puyi, the last Emperor of China. He was also the last British Administrator of Weihaiwei.

雷金纳德·弗莱明·庄士敦爵士,KCMG,CBE(英语:Sir Reginald Fleming Johnston,1874年-10月13日-1938年-3月6日),汉名庄士敦,字志道,英国苏格兰爱丁堡人,毕业于爱丁堡大学及牛津大学,中国清朝末代皇帝溥仪之外籍帝师。


History.

DTU was founded in 1829 as the "College of Advanced Technology" (Danish: Den Polytekniske Læreanstalt) with the physicist Hans Christian Ørsted, then a professor at the University of Copenhagen, as one of the driving forces. The inspiration was the École Polytechnique in Paris, France which Ørsted had visited as a young scientist. The new institution was inaugurated on 5 November 1829 with Ørsted as its principal, a position he held until his death in 1851. The new college's first home was two buildings in Studiestræde and St- Pederstræde in central Copenhagen. Although expanded several times, they remained inadequate and in 1890 a new building complex was inaugurated in Sølvgade in 1890. The new buildings were designed by the architect Johan Daniel Herholdt.  In 1903, the College of Advanced Technology commenced the education of electrical engineers in addition to the construction engineers, production engineers, and mechanical engineers already educated at the college.  In the 1920s, space had once again become insufficient and in 1929 the foundation stone was laid for a new school at Østervold. Completion of the building was delayed by World War II and it was not completed until 1954.  From 1933, the institution was officially known as "Danmarks tekniske Højskole (DtH)", which was usually translated as the 'Technical University of Denmark'. On 1 April 1994, in connection with the joining of "Danmarks Ingeniørakademi" (DIA) and DTH, the Danish name was changed to "Danmarks Tekniske Universitet", in order to include the word 'University', thus giving rise to the initials DTU by which the university is commonly known today. The formal name, "Den Polytekniske Læreanstalt, Danmarks Tekniske Universitet", still includes the original name.  In 1960 a decision was made to move the College of Advanced Technology to new and larger facilities in Lyngby north of Copenhagen. They were inaugurated on 17 May 1974.  On 23 and 24 November 1967, the University Computing Center hosted the NATO Science Committee's Study Group first meeting discussing the newly coined term "Software Engineering".  On 1 January 2007, the university was merged with the following Danish research centers: Forskningscenter Risø, Danmarks Fødevareforskning, Danmarks Fiskeriundersøgelser (from 1 January 2008: National Institute for Aquatic Resources; DTU Aqua), Danmarks Rumcenter, and Danmarks Transport-Forskning.

Organization and administration.

The university is governed by a board consisting of 10 members: six members recruited outside the university form the majority of the board, one member is appointed by the scientific staff, one member is appointed by the administrative staff, and two members are appointed by the university students.  The President of DTU is appointed by the university board. The president in turn appoints deans, and deans appoint heads of departments.  In 2014, DTU was granted an institutional accreditation by the Danish Accreditation Institution (member of ENQA). The institutional accreditation ensures that the quality assurance system of the institution is well-described, well-argued, and well-functioning in practice.  Since DTU has no faculty senate, and since the faculty is not involved in the appointment of president, deans, or department heads, the university has no faculty governance.

Campus.

The university is located on a plain known as Lundtoftesletten in the northeastern end of the city of Lyngby. The area was previously home to the airfield Lundtofte Flyveplads.  The campus is roughly divided in half by the road Anker Engelunds Vej going in the east-west direction, and, perpendicular to that, by two lengthy, collinear roads located on either side of a parking lot. The campus is thus divided into four parts, referred to as quadrants, numbered 1 through 4 in correspondence with the conventional numbering of quadrants in the Cartesian coordinate system with north upwards.

Controversy.

DTU was the subject of controversy in 2009 because the (then) institute director of the Department of Chemistry, O.W. Sørensen, was a high-ranking member of Scientology. In relation to this, the university was accused of violating the principles of free speech by threatening to fire employees, among them Rolf W. Berg, who voiced their criticism of the institute director. On 7 April 2010, the successor of Sørensen was announced, at a department meeting, as Erling Stenby, who officially took over as Director on 1 May 2010.

Rankings.

The university maintains an updated site with the university's standing in several relevant academic and research rankings. In November 2007 the "Times Higher Education Supplement" put the university as number 130 in their ranking of the universities of the world and number 122 in 2010.

Extracurricular organizations.

Sports.

Exiles RUFC is the official rugby union club of DTU.

Student organizations.

168-year-old Polyteknisk Forening, as well as the maritime student association Nul-kryds formed in 1947.

The Technical University of Denmark (), often simply referred to as DTU, is a university in Kongens Lyngby, north of central Copenhagen, Denmark. It was founded in 1829 at the initiative of Hans Christian Ørsted as Denmark's first polytechnic, and is today ranked among Europe's leading engineering institutions.

丹麦技术大学(,缩写:DTU),是丹麦培养高级工程技术人员的主要学府,北欧最顶尖的理工大学,是欧洲卓越理工大学联盟、北欧五校联盟成员之一,坐落于丹麦首都哥本哈根北部的灵比。


History.

The Irish Guards were formed on 1 April 1900 by order of Queen Victoria to commemorate the Irishmen who fought in the Second Boer War for the British Empire.

First World War.

Following the outbreak of the First World War, 1st Battalion Irish Guards was deployed to France almost immediately, and they remained on the Western Front for the duration of the war. During the early part of the war, the Battalion took part in the Battle of Mons and formed the Allied rearguard during the Great Retreat. The Battalion then took part in one of the bloodiest battles of 1914, the First Battle of Ypres, which began on 19 October, inflicting major casualties among the old Regular Army.  The 1st Battalion was involved in fighting for the duration of 'First Ypres', at Langemarck, Gheluvelt and Nonne Bosschen. The 1st Battalion suffered huge casualties between 1–8 November holding the line against near defeat by German forces, while defending Klein Zillebeke.  In May 1915, the 1st Battalion took part in the Battle of Festubert, though did not see much action. Two further battalions were formed for the regiment in July. In September that year, all three battalions took part in the Battle of Loos, which lasted from 25 September until early October.  The Irish Guards went into action again on 1 July 1916 when the Battle of the Somme began. The 1st Battalion took part in an action at Flers–Courcelette where they suffered severe casualties in the attack in the face of withering fire from the German machine-guns. The Battalion also took part in the action at Morval before they were relieved by the 2nd Battalion.  In 1917 the Irish Guards took part in the Battle of Pilckem which began on 31 July during the Third Battle of Ypres. The Irish Guards also took part in the Battle of Cambrai that year. In 1918 the regiment fought in a number of engagements during the Second Battle of the Somme, including at Arras and Albert. The regiment then went on to take part in a number of battles during the British offensives against the Hindenburg Line. On 11 November 1918 the Armistice with Germany was signed. The 1st Battalion was at Maubeuge when the Armistice was signed.  The regiment's continued existence was threatened briefly when Winston Churchill, who served as Secretary of State for War between 1919 and 1921, sought the elimination of the Irish Guards and Welsh Guards as an economy measure. This proposal, however, did not find favour in government or army circles and was dropped. Between the wars, the regiment was deployed at various times to Turkey, Gibraltar, Egypt and Palestine.

Second World War.

During the Second World War, the regiment fought in Norway, France, North Africa, Italy, Belgium, Netherlands and Germany. The regiment first saw combat during the Norwegian Campaign. Following a challenging sea voyage to Norway, the 1st Battalion arrived in May 1940 and fought for two days at the town of Pothus before they were forced to retreat. The Irish Guards conducted a fighting withdrawal and served as the Allied rearguard.  The Battalion was evacuated along with the rest of the expeditionary force in June. While the 1st Battalion was fighting in Norway, the 2nd Battalion was deployed to the Hook of Holland to cover the evacuation of the Dutch Royal Family and Government in May 1940. The 2nd Battalion was then deployed to France and ordered to defend the port of Boulogne. The guardsmen held out against overwhelming odds for three days, buying valuable time for the Dunkirk Evacuation, before they were evacuated themselves. In November 1942, during the Second World War, Jean, Grand Duke of Luxembourg joined the British Army as a volunteer in the Irish Guards.  In March 1943 the 1st Battalion landed, with the rest of the 24th Guards Brigade, in Tunisia, to fight in the final stages of the campaign in North Africa. The Battalion saw extensive action while fighting through Tunisia and was subsequently deployed to the Italian Front in December of that year. The Battalion took part in the Anzio landings on 22 January 1944. They also participated in the fierce fighting around the Allied beachhead and suffered severe casualties fighting off a German counterattack at Campoleone after which the depleted battalion was returned to the UK in April.  The Irish Guards returned to France in June 1944 when the 2nd and 3rd Battalions took part in the Normandy Campaign. Both battalions served as part of the Guards Armoured Division and took part in the attempt to capture Caen as part of Operation Goodwood. They also saw action in the Mont Pincon area. On 29 August, the 3rd Battalion crossed the Seine and began the advance into Belgium with the rest of the Guards Armoured Division towards Brussels.  The Irish Guards were part of the ground force of Operation Market Garden, 'Market' being the airborne assault and 'Garden' the ground attack. The Irish Guards led the vanguard of XXX Corps in their advance towards Arnhem, which was the objective of the British 1st Airborne Division, furthest from XXX Corps' start line. The Corps crossed the Belgian-Dutch border, advancing from Neerpelt on 17 September but the Irish Guards encountered heavy resistance which slowed the advance. Following the conclusion of Market Garden, the Irish Guards remained in the Netherlands until taking part in the Allied advance into Germany and seeing heavy action during the Rhineland Campaign with Guardsman Edward Charlton winning the final Victoria Cross to be awarded in the European theatre.

1945 - 2019.

After the war, the regiment was reduced to a single battalion. In 1947, the 1st Battalion deployed to Palestine to perform internal security duties there. It was then posted to the Suez Canal Zone in Egypt, remaining there until the British withdrawal in 1956. The regiment continued to serve in troubled regions such as Cyprus and Aden throughout the 1950s and 1960s. During this time they were also part of the British Army of the Rhine (BAOR) in Germany on a number of occasions. They also served as the garrison of Hong Kong from 1970 to 1972.  The Irish Guards were one of the few regiments in the British Army initially exempt from service in Northern Ireland during The Troubles. However, a Provisional Irish Republican Army (IRA) bomb blasted a bus carrying members of the regiment band to Chelsea Barracks in October 1981. 39 people (23 soldiers and 16 others) were wounded and two civilians were killed. 1992 saw the regiment finally carry out its first tour-of-duty in Northern Ireland, based in County Fermanagh.  The Irish Guards were involved in the Balkans Conflicts when they were deployed to Macedonia and Kosovo in 1999 and were the first British unit to enter the Kosovan capital city of Pristina on 12 June. The regiment played a significant role in the initial stages of the Iraq War as part of the 7th Armoured Brigade and they led the British advance into Basra in March 2003. The Irish Guards deployed to Iraq on Operation Telic 10 in 2007. In 2010, the regiment deployed on their first tour of duty to Afghanistan. Number 2 Company deployed to Afghanistan in 2013 as a Brigade Operations Company.  In 2014 the entire regiment deployed to Cyprus to patrol the buffer zone as part of Operation Tosca 20. Following the Manchester Arena bombing, the Irish Guards were deployed in London to guard key locations, including the Ministry of Defence building in Whitehall, as part of Operation Temperer. Later that year Number 1 Company deployed to the Falkland Islands as the Roulement Infantry Company while Number 2 Company deployed to Thailand on an overseas training exercise where they worked alongside the Thai Army.

2019/20.

December 2019 saw the Irish Guards deploy on two operations concurrently. Number 1 Company deployed to South Sudan on Operation Trenton and the rest of the Battalion deployed to Iraqon Operation Shader, training Iraqi Security Forces in the mission to defeat Daesh. However, the deployment rapidly changed in January 2020 with the escalation of the 2019–20 Persian Gulf crisis following the American strike on Major General Qasem Soleimani. The Irish Guards' mission changed from training to force protection in order to protect British assets in Iraq from possible retaliation by Iran. Eventual de-escalation saw the Irish Guards resume their original mission.  As a result of the Army 2020 Refine reforms, the Irish Guards are in the process of relocating from Cavalry Barracks, Hounslow to Mons Barracks at Aldershot Garrison.

Current role and organisation.

The 1st Battalion Irish Guards is broken down into five separate Companies; No 1, No 2, No 3 and No 4 Companies, along with the Headquarters Company.

Recruitment.

Although restrictions in Ireland's Defence Act make it illegal to induce, procure or persuade enlistment of any citizen of Ireland into the military of another state, people from the Republic do frequently enlist in the Regiment.

Uniform.

Like the other Guards regiments, the "Home Service Dress" of the Irish Guards is a scarlet tunic and bearskin. Buttons are worn in fours, reflecting the regiment's position as the fourth most senior Guards regiment, and the collar is adorned with embroided shamrock. They also sport a St. Patrick's blue plume on the right side of the bearskin.  A plume of St Patrick's blue was selected because blue is the colour of the mantle and sash of the Order of St Patrick, a chivalric order, founded by George III of the United Kingdom for the Kingdom of Ireland in February 1783 from which the regiment also draws its cap star and motto.  In "Walking-out Dress", the Irish Guards can be identified by the green band on their forage caps. Officers also traditionally carry a blackthorn pace stick. Like the other Guards regiments, they wear a khaki beret with the blue/red/blue Household Division backing patch on it. On the beret, ranks from Guardsman to Lance Sergeant wear a brass or staybrite cap badge, Sergeants and Colour Sergeants wear a bi-metal cap badge, Warrant Officers wear a silver plate gilt and enamel cap badge and commissioned officers of the regiment wear an embroidered cap badge.  The Irish Guards pipers wear saffron kilts, green hose with saffron flashes and heavy black shoes known as brogues with no spats, a rifle green doublet with buttons in fours and a hat known as a caubeen.The regimental capstar is worn over the piper's right eye and is topped by a blue hackle. A green cloak with four silver buttons is worn over the shoulders and is secured by two green straps that cross over the chest.  Prince William, Duke of Cambridge, who is Colonel of the Irish Guards, wore the uniform of the Irish Guards at his wedding to Catherine, Duchess of Cambridge.

Motto.

The regiment takes its motto, "Quis Separabit", or "Who shall separate us?" from the Order of St Patrick.

Nickname.

The Irish Guards are known affectionately throughout the British Army as "the Micks" or "Fighting Micks." An earlier nickname, "Bob's Own", after Field Marshal Lord Roberts has fallen into disuse. The term "Micks", while generally derogatory in civilian life, is embraced in the context of the Irish Guards' nickname.

Training.

Recruits to the Guards Division go through a thirty-week training programme at the Infantry Training Centre (ITC). The training is two weeks more than the training for the Regular line infantry regiments of the British Army; the extra training, carried out throughout the course, is devoted to drill and ceremonies.

Mascot.

Since 1902, an Irish Wolfhound has been presented as a mascot to the regiment by the Irish Wolfhound Club, who originally hoped the publicity would increase the breed's popularity with the public. The first mascot was called Brian Boru.  In 1961, the wolfhound was admitted to the select club of "official" Army mascots, entitling him to the services of the Royal Army Veterinary Corps, as well as quartering and food at public expense. Originally, the mascot was in the care of a drummer boy, but is now looked after by one of the regiment's drummers and his family. The Irish Guards are the only Guards regiment permitted to have their mascot lead them on parade. During Trooping the Colour, the mascot marches only from Wellington Barracks as far as Horse Guards Parade. He then falls out of the formation and does not participate in the Trooping itself. Domhnall, the regiment's seventeenth mascot, retired back to Ireland, in 2019.

Traditions and affiliations.

St. Patrick's Day is the traditional regimental celebration. It is customary for the regiment to begin the day's celebrations with the Guardsmen being woken by their officers and served gunfire. Fresh shamrock is then presented to members of the regiment, whether they are in the UK or abroad on operations.  Except in wartime, the presentation of shamrock is traditionally made by a member of the Royal Family. This task was first performed in 1901 by Queen Alexandra and later by Queen Elizabeth The Queen Mother. After the latter's death, the presentation was made by The Princess Royal. Starting in 2012, the presentation has been made by the Duchess of Cambridge.  In 1950 King George VI marked the fiftieth anniversary of the formation of the Irish Guards by presenting the Shamrocks on St Patrick ́s Day. This honour was mirrored by King George's surviving wife, Queen Elizabeth The Queen Mother, fifty years later when she presented shamrocks to the regiment on St. Patrick's Day in their centenary year of 2000.

Battle honours.

The regiment's battle honours are as follows:

Regimental Colonels.

British Army regiments typically have an honorary "colonel", often a member of the Royal Family or a prominent retired military officer with connections to the regiment.  The Irish Guards colonels have been:

Colonels Commanding, Irish Guards.

Colonels commanding Irish Guards have included:

Commanding Officers.

Commanding Officers have included (since 2001):

Alliances.

The Irish Guards enjoys a Bond of Friendship with 13th Demi-Brigade of the Foreign Legion. This official affiliation stems from the shared history of the two regiments. They both fought together in Taskforce Rupert during the 1940 Norwegian campaign.  The Irish Guards and other Guards regiments have a long-standing connection to The Parachute Regiment. Irish Guardsmen who have completed P Company can be seconded to the Guards Parachute Platoon, which is currently attached to the 3rd Battalion, The Parachute Regiment. The Guards Parachute Platoon maintains the tradition established by Number 1 (Guards) Independent Parachute Company that was part of the original Pathfinder Group of 16th Parachute Brigade, which has since been designated as the 16th Air Assault Brigade.

The Irish Guards (IG), part of the Guards Division, is one of the Foot Guards regiments of the British Army and, together with the Royal Irish Regiment, it is one of the two Irish infantry regiments in the British Army. The regiment has participated in campaigns in the First World War, the Second World War, the Iraq War and the War in Afghanistan as well as numerous other operations throughout its history. The Irish Guards claim six Victoria Cross recipients, four from the First World War and two from the Second World War.

爱尔兰卫队(英语:Irish Guards,简称IG)是英国的卫兵师之一,也是英国陆军的一部分,和皇家爱尔兰军团并为英国陆军现在仅有的两个爱尔兰步兵团之一。爱尔兰卫队主要在北爱尔兰和英国的爱尔兰人社区招募队员。虽然爱尔兰共和国法律规定爱尔兰公民参加其他国家军队违法,但现在爱尔兰卫队有四人来自爱尔兰共和国。