Categoricity of an abstract elementary class in two successive cardinals

Details Categoricity of an abstract elementary class in two successive cardinals Categoricity of an abstract elementary class in two successive cardinals

1998-05-15

arxiv.org/abs/math/9805146v1

Mathematics

Logic

Scientific paper

We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models or existence of large cardinals). We prove (assuming a weak version of GCH around lambda) that if K is categorical in lambda, lambda^+, LS(K) <= lambda and 1 <= I(lambda^{++},K)< 2^{lambda^{++}} then K has a model in lambda^{+++} .

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