BETWEEN REDUCED POWERS AND ULTRAPOWERS, II

Ilijas Farah, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fréchet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

Original languageEnglish
Pages (from-to)9007-9034
Number of pages28
JournalTransactions of the American Mathematical Society
Volume375
Issue number12
DOIs
StatePublished - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society.

Keywords

  • Cohen model
  • Continuum Hypothesis
  • Proper Forcing Axiom
  • reduced powers
  • saturated models
  • small basis
  • Ultrapowers
  • universal models

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