Categoricity and solvability of A.E.C., quite highly
Logic
2008-08-25 v1
Abstract
We investigate in ZFC what can be the family of large enough cardinals mu in which an a.e.c. K is categorical or even just solvable. We show that for not few cardinals lambda<mu there is a superlimit model in K_lambda. Moreover, our main result is that we can find a good lambda-frame s categorical in lambda such that K_s subseteq K_lambda. We then show how to use [Sh:705] to get categoricity in every large enough cardinality if K has cases of mu-amalgamation for enough mu and 2^mu<2^{mu^{+1}} <... < 2^{mu^{+n}}... for enough mu.
Keywords
Cite
@article{arxiv.0808.3023,
title = {Categoricity and solvability of A.E.C., quite highly},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:0808.3023},
year = {2008}
}