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

M. Malliaris*, S. Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Solving a decades-old problem we show that Keisler's 1967 order on theories has the maximum number of classes. In fact, it embeds P(ω)/fin. 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 Szemerédi's regularity lemma. The proof involves ideas from model theory, set theory, and finite combinatorics.

Original languageEnglish
Article number108036
JournalAdvances in Mathematics
Volume392
DOIs
StatePublished - 3 Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Keisler's order
  • Model theory
  • Regular ultrafilters
  • Simple theories

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