Categoricity of an abstract elementary class in two successive cardinals
Saharon Shelah
Abstract
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)< 2lambda++ then K has a model in lambda+++ .
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