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- W3086877267 abstract "We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. 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. This 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 analog of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories." @default.
- W3086877267 created "2020-09-21" @default.
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- W3086877267 date "2022-09-27" @default.
- W3086877267 modified "2023-09-25" @default.
- W3086877267 title "Exact saturation in pseudo-elementary classes for simple and stable theories" @default.
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- W3086877267 doi "https://doi.org/10.1142/s0219061322500209" @default.
- W3086877267 hasPublicationYear "2022" @default.
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