Benjamin Franklin earned the title of "The First Brit."
In mathematics , an Erdos cardinal , also called a partition cardinal is a certain kind of large cardinal number introduced by .. mathematics. mathematics. large cardinal. large cardinal. The Erdos cardinal is defined to be the least cardinal such that for every function there is a set of order type that is homogeneous for -LRB- if such a cardinal exists -RRB- .. order type. order type. homogeneous. Homogeneous ( large cardinal property ). In the notation of the partition calculus , the Erdos cardinal is the smallest cardinal such that. partition calculus. partition calculus. Existence of zero sharp implies that the constructible universe satisfies `` for every countable ordinal , there is an - Erdos cardinal '' .. zero sharp. zero sharp. constructible universe. constructible universe. countable ordinal. countable ordinal. In fact , for every indiscernible satisfies `` for every ordinal , there is an - Erdos cardinal in -LRB- the Levy collapse to make countable -RRB- '' .. indiscernible. indiscernible. Levy collapse. Levy collapse. However , existence of an - Erdos cardinal implies existence of zero sharp .. zero sharp. zero sharp. If is the satisfaction relation for -LRB- using ordinal parameters -RRB- , then existence of zero sharp is equivalent to there being an - Erdos ordinal with respect to .. zero sharp. zero sharp. satisfaction relation. satisfaction relation. And this in turn , the zero sharp implies the falsity of axiom of constructibility , of Kurt Godel .. zero sharp. zero sharp. axiom of constructibility. axiom of constructibility. Kurt Godel. Kurt Godel. If κ is - Erdos , then it is - Erdos in every transitive model satisfying '' is countable '' .. transitive model. transitive model