Exact saturation in pseudo-elementary classes for simple and stable theories
release_lkdge53rkzf6ni34tthi4mzoca
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Itay Kaplan, Nicholas Ramsey, Saharon Shelah
2020
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.
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2009.08365v1
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