The Keisler–Shelah isomorphism theorem and the continuum hypothesis II

Mohammad Golshani*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We continue the investigation started in Golshani (2021) about the relation between the Keilser–Shelah isomorphism theorem and the continuum hypothesis. In particular, we show it is consistent that the continuum hypothesis fails and for any given sequence m=⟨(Mn1,Mn2):n<ω⟩ of models of size at most ℵ1 in a countable language, if the sequence satisfies a mild extra property, then for every non-principal ultrafilter D on ω, if the ultraproducts ∏DMn1 and ∏DMn2 are elementarily equivalent, then they are isomorphic.

Original languageEnglish
Pages (from-to)789-801
Number of pages13
JournalMonatshefte fur Mathematik
Volume201
Issue number3
DOIs
StatePublished - Jul 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.

Keywords

  • Forcing
  • The continuum hypothesis
  • The Keisler-Shelah isomorphism theorem
  • Ultraproduct

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