# Sh:1197

• Kaplan, I., Ramsey, N., & Shelah, S. Exact saturation in pseudo elementary classes for simple and stable theories. Preprint. arXiv: 2009.08365
• 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.
• Version 2020-09-18 (25p)
Bib entry
@article{Sh:1197,
author = {Kaplan, Itay and Ramsey, Nicholas and Shelah, Saharon},
title = {{Exact saturation in pseudo elementary classes for simple and stable theories}},
note = {\href{https://arxiv.org/abs/2009.08365}{arXiv: 2009.08365}},
arxiv_number = {2009.08365}
}