Categoricity from one successor cardinal in Tame Abstract Elementary Classes
Logic
2007-05-23 v1
Abstract
Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is \chi-tame. If K is categorical in some \lambda^+ >LS(K) then it is categorical in all \mu\geq (\lambda+\chi)^+. Theorem 2. If K is LS(K)-tame and is categorical both in LS(K) and in LS(K)^+ then K is categorical in all \mu\geq LS(K).
Keywords
Cite
@article{arxiv.math/0510004,
title = {Categoricity from one successor cardinal in Tame Abstract Elementary Classes},
author = {Rami Grossberg and Monica VanDieren},
journal= {arXiv preprint arXiv:math/0510004},
year = {2007}
}
Comments
20 pages