Categoricity of an abstract elementary class in two successive cardinals
Logic
2016-09-07 v1
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)< 2^{lambda^{++}} then K has a model in lambda^{+++} .
Keywords
Cite
@article{arxiv.math/9805146,
title = {Categoricity of an abstract elementary class in two successive cardinals},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9805146},
year = {2016}
}