Keisler's order has infinitely many classes

DOI10.1007/s11856-018-1647-7zbMath1402.03045arXiv1503.08341OpenAlexW2964290384WikidataQ105488020 ScholiaQ105488020MaRDI QIDQ1650013

Saharon Shelah, Maryanthe Malliaris

Publication date: 29 June 2018

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.08341

zbMATH Keywords

Keisler's order

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20) Abstract model theory (03C95)

Related Items (15)

Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Cofinality spectrum problems: the axiomatic approach ⋮ Model-theoretic applications of cofinality spectrum problems ⋮ KEISLER’S ORDER IS NOT LINEAR, ASSUMING A SUPERCOMPACT ⋮ 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 ⋮ Existence of optimal ultrafilters and the fundamental complexity of simple theories ⋮ 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) ⋮ The first omega alephs: from simplices to trees of trees to higher walks ⋮ A separation theorem for simple theories

Cites Work

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• Independence, order, and the interaction of ultrafilters and theories
• Existence of optimal ultrafilters and the fundamental complexity of simple theories
• Realization of \(\varphi \)-types and Keisler's order
• Combinatorial set theory: Partition relations for cardinals
• Regularity of ultrafilters and the core model
• Classification theory and the number of non-isomorphic models.
• Set mappings on 4-tuples
• Ultraproducts in the theory of models
• A dividing line within simple unstable theories
• Good ideals in fields of sets
• Constructing regular ultrafilters from a model-theoretic point of view
• Stable group theory and approximate subgroups
• Cofinality spectrum theorems in model theory, set theory, and general topology
• Two consistency results on set mappings
• Model theory and the cardinal numbers 𝔭 and 𝔱
• General topology meets model theory, on 𝔭 and 𝔱
• Some theorems of set theory and their topological consequences
• Ultraproducts which are not saturated
• Ultrafilters and Independent Sets

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