Exact saturation in pseudo-elementary classes for simple and stable theories
Logic
2022-05-10 v2
Abstract
We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals, satisfying mild set-theoretic hypotheses, which had previously been open even for the random graph. We characterize supersimplicity of countable theories in terms of having PC-exact saturation at singular cardinals of countable cofinality. We also consider the local analogue of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories.
Keywords
Cite
@article{arxiv.2009.08365,
title = {Exact saturation in pseudo-elementary classes for simple and stable theories},
author = {Itay Kaplan and Nicholas Ramsey and Saharon Shelah},
journal= {arXiv preprint arXiv:2009.08365},
year = {2022}
}