The Keisler–Shelah isomorphism theorem and the continuum hypothesis II

Mohammad Golshani; Saharon Shelah

doi:10.1007/s00605-023-01837-y

The Keisler–Shelah isomorphism theorem and the continuum hypothesis II

Mohammad Golshani^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	789-801
Number of pages	13
Journal	Monatshefte fur Mathematik
Volume	201
Issue number	3
DOIs	https://doi.org/10.1007/s00605-023-01837-y
State	Published - 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 Keisler-Shelah isomorphism theorem
The continuum hypothesis
Ultraproduct

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10.1007/s00605-023-01837-y

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AB - 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.

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The Keisler–Shelah isomorphism theorem and the continuum hypothesis II

Abstract

Bibliographical note

Keywords

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