MODEL-THEORETIC PROPERTIES OF ULTRAFILTERS BUILT BY INDEPENDENT FAMILIES OF FUNCTIONS

DOI10.1017/jsl.2013.28zbMath1338.03055arXiv1208.2579OpenAlexW2962679058MaRDI QIDQ2921022

Saharon Shelah, Maryanthe Malliaris

Publication date: 30 September 2014

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.2579

zbMATH Keywords

regular ultrafilterssaturation of ultrapowersKeisler orderunstable model theory

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20)

Related Items (8)

Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Constructing regular ultrafilters from a model-theoretic point of view ⋮ Atomic saturation of reduced powers ⋮ On cuts in ultraproducts of linear orders I ⋮ Some simple theories from a Boolean algebra point of view ⋮ Existence of optimal ultrafilters and the fundamental complexity of simple theories ⋮ A dividing line within simple unstable theories ⋮ ON CUTS IN ULTRAPRODUCTS OF LINEAR ORDERS II

Cites Work

• Realization of \(\varphi \)-types and Keisler's order
• Combinatorial set theory: Partition relations for cardinals
• On \(\vartriangleleft^{*}\)-maximality.
• Toward classifying unstable theories
• A dividing line within simple unstable theories
• Good ideals in fields of sets
• Regular ultrafilters and finite square principles
• Some theorems of set theory and their topological consequences

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