Keisler's order is not simple (and simple theories may not be either)

DOI10.1016/J.AIM.2021.108036arXiv1906.10241MaRDI QIDQ6320997

Publication date: 24 June 2019

Abstract: Solving a decades-old problem we show that Keisler's 1967 order on theories has the maximum number of classes. The theories we build are simple unstable with no nontrivial forking, and reflect growth rates of sequences which may be thought of as densities of certain regular pairs, in the sense of Szemer'edi's regularity lemma. The proof involves ideas from model theory, set theory, and finite combinatorics.

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Random graphs (graph-theoretic aspects) (05C80) Other combinatorial set theory (03E05) Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20)

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