A dividing line within simple unstable theories

DOI10.1016/j.aim.2013.08.027zbMath1323.03042arXiv1208.2140OpenAlexW2962951999MaRDI QIDQ2450799

Saharon Shelah, Maryanthe Malliaris

Publication date: 16 May 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.2140

zbMATH Keywords

unstable theoriesKeisler's ordergood filterssaturation of regular ultrapowers

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Other combinatorial set theory (03E05) Classification theory, stability, and related concepts in model theory (03C45) Models with special properties (saturated, rigid, etc.) (03C50) Ultraproducts and related constructions (03C20)

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Cites Work

• Independence, order, and the interaction of ultrafilters and theories
• More on \(\mathrm{SOP}_1\) and \(\mathrm{SOP}_2\)
• Realization of \(\varphi \)-types and Keisler's order
• Classification theory and the number of non-isomorphic models.
• Classification theory and the number of non-isomorphic models
• Model theory
• A primer of simple theories
• On \(\vartriangleleft^{*}\)-maximality.
• Toward classifying unstable theories
• Good ideals in fields of sets
• MODEL-THEORETIC PROPERTIES OF ULTRAFILTERS BUILT BY INDEPENDENT FAMILIES OF FUNCTIONS
• Constructing regular ultrafilters from a model-theoretic point of view
• The characteristic sequence of a first-order formula
• Cofinality spectrum theorems in model theory, set theory, and general topology
• Simple unstable theories
• Lascar strong types in some simple theories
• Hypergraph sequences as a tool for saturation of ultrapowers
• Some theorems of set theory and their topological consequences
• Ultraproducts which are not saturated
• Ultrafilters and Independent Sets
• A supersimple nonlow theory