Sh:1197
- Kaplan, I., Ramsey, N., & Shelah, S. (2023). Exact saturation in pseudo-elementary classes for simple and stable theories. J. Math. Log., 23(2), Paper No. 2250020, 26. arXiv: 2009.08365 DOI: 10.1142/S0219061322500209 MR: 4575271
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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) published version (26p)
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}},
journal = {J. Math. Log.},
fjournal = {Journal of Mathematical Logic},
volume = {23},
number = {2},
year = {2023},
pages = {Paper No. 2250020, 26},
issn = {0219-0613},
mrnumber = {4575271},
mrclass = {03C45 (03C55)},
doi = {10.1142/S0219061322500209},
note = {\href{https://arxiv.org/abs/2009.08365}{arXiv: 2009.08365}},
arxiv_number = {2009.08365}
}