Existence of optimal ultrafilters and the fundamental complexity of simple theories

DOI10.1016/j.aim.2015.12.009zbMath1431.03048arXiv1404.2919OpenAlexW2963220768WikidataQ105488011 ScholiaQ105488011MaRDI QIDQ908076

Saharon Shelah, Maryanthe Malliaris

Publication date: 2 February 2016

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

Full work available at URL: https://arxiv.org/abs/1404.2919

zbMATH Keywords

model theoryultrafiltersclassification of simple theoriesKeisler's orderoptimal ultrafilterssaturation of ultrapowers

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Classification theory, stability, and related concepts in model theory (03C45) Chain conditions, complete algebras (06E10) Logical aspects of Boolean algebras (03G05) Ultraproducts and related constructions (03C20)

Related Items (18)

Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Cofinality spectrum problems: the axiomatic approach ⋮ Keisler's order has infinitely many classes ⋮ Model-theoretic applications of cofinality spectrum problems ⋮ KEISLER’S ORDER IS NOT LINEAR, ASSUMING A SUPERCOMPACT ⋮ COMPACT CARDINALS AND EIGHT VALUES IN CICHOŃ’S DIAGRAM ⋮ Atomic saturation of reduced powers ⋮ Using ultrapowers to compare continuous structures ⋮ Some simple theories from a Boolean algebra point of view ⋮ Open problems on ultrafilters and some connections to the continuum ⋮ The Keisler order in continuous logic ⋮ THE TURING DEGREES AND KEISLER’S ORDER ⋮ A new look at interpretability and saturation ⋮ On positive local combinatorial dividing-lines in model theory ⋮ An example of a new simple theory ⋮ Keisler's order is not simple (and simple theories may not be either) ⋮ Cichoń's maximum ⋮ A separation theorem for simple theories

Cites Work

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• Realization of \(\varphi \)-types and Keisler's order
• Classification theory and the number of non-isomorphic models.
• A primer of simple theories
• Keisler's order has infinitely many classes
• Ultraproducts in the theory of models
• A dividing line within simple unstable theories
• Good ideals in fields of sets
• Diophantine problems over local fields. III: Decidable fields
• Every two elementarily equivalent models have isomorphic ultrapowers
• MODEL-THEORETIC PROPERTIES OF ULTRAFILTERS BUILT BY INDEPENDENT FAMILIES OF FUNCTIONS
• Constructing regular ultrafilters from a model-theoretic point of view
• Good and Ok Ultrafilters
• Cofinality spectrum theorems in model theory, set theory, and general topology
• Reduced direct products
• Model theory and the cardinal numbers 𝔭 and 𝔱
• General topology meets model theory, on 𝔭 and 𝔱
• Hypergraph sequences as a tool for saturation of ultrapowers
• Diophantine Problems Over Local Fields I
• Some theorems of set theory and their topological consequences
• Ultraproducts which are not saturated
• Saturation of ultrapowers and Keisler's order
• Ultrafilters and Independent Sets

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