Independence, order, and the interaction of ultrafilters and theories

DOI10.1016/J.APAL.2011.12.010zbMath1279.03060OpenAlexW2067589138MaRDI QIDQ450953

Maryanthe Malliaris

Publication date: 26 September 2012

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2011.12.010

zbMATH Keywords

independence propertyregular ultrapowersunstable theories

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Ultraproducts and related constructions (03C20)

Related Items (8)

Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Cofinality spectrum problems: the axiomatic approach ⋮ Keisler's order has infinitely many classes ⋮ Constructing regular ultrafilters from a model-theoretic point of view ⋮ Open problems on ultrafilters and some connections to the continuum ⋮ A dividing line within simple unstable theories ⋮ Keisler's order is not simple (and simple theories may not be either) ⋮ General topology meets model theory, on 𝔭 and 𝔱

Cites Work

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• On \(\vartriangleleft^{*}\)-maximality.
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• There are just four second-order quantifiers
• Ultraproducts in the theory of models
• The characteristic sequence of a first-order formula
• Homogeneous Universal Models.
• Simple unstable theories
• On sets of integers containing k elements in arithmetic progression
• Hypergraph sequences as a tool for saturation of ultrapowers
• Ultraproducts which are not saturated
• Ultrafilters and Independent Sets

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