Campo Cerrado — forest or savanna?
Today it is undisputed that living systems contain information for the interpretation of the developmental history or the recent growth potential of an area. The decoding of this information, important for the research on landscapes, can only be managed by consequent clarification of the chorological, population-genetic and autecological particularities of the organisms in the landscapes (MÜLLER 1976, 1977). The importance of this biogeographical concept for the evaluation of our landscapes can be shown using the example of the Campos Cerrados, which are increasingly being considered for exploitation and which were defined either as “forest formations” or “savanna types” from the turn of the century until recent days.
GEOGRAPHY OF THE SIBLING SPECIES RELATED TO DROSOPHILA WILLISTONI, AND OF THE SEMISPECIES OF THE DROSOPHILA PAULISTORUM COMPLEX
The six sibling species of Drosophila willistoni group are among the most favorable, and at the same time challenging materials for studies on the genetics of speciation processes. The species are D. willistoni Sturtevant, D. paulistorum Dobzhansky & Pavan, D. pavlovskiana Kastritsis & Dobzhansky, D. equinoxialis Dobzhansky, D. tropicalis Burla & da Cunha, and D. insularis Dobzhansky. Burla et al. (1949) found slight morphological differences that were insufficient for identification of single individuals, but Spassky (1957) noted differences in the male genitalia which do permit such identification. Unambiguous discrimination is also possible through examination of the gene arrangements in the chromosomes of larval salivary glands (Burla et al., 1949; Dobzhansky et al., 1950), and of the variant enzymes detected by electrophoresis (Ayala et al., 1970). Owing to ethological isolation, crossmating of the species occurs rarely, although under laboratory conditions some cross-inseminations can be obtained (Burla et al., 1949). Intercrosses of D. insularis females with D. tropicalis and D. willistoni males, and occasionally with D. paulistorum
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.