The Keisler–Shelah isomorphism theorem and the continuum hypothesis

Mohammad Golshani; Saharon Shelah

doi:10.4064/fm198-5-2022

The Keisler–Shelah isomorphism theorem and the continuum hypothesis

Mohammad Golshani, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that if for any two elementary equivalent structures M,N of size at most continuum in a countable language, M^ω/U ≃ N^ω/U for some ultrafilter U on ω, then CH holds. We also provide some consistency results related to Keisler and Shelah isomorphism theorems in the absence of CH.

Original language	English
Pages (from-to)	59-66
Number of pages	8
Journal	Fundamenta Mathematicae
Volume	260
DOIs	https://doi.org/10.4064/fm198-5-2022
State	Published - 2023

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2023.

Keywords

Keisler–Shelah isomorphism theorem
forcing
the continuum hypothesis
ultrapowers

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10.4064/fm198-5-2022

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The Keisler–Shelah isomorphism theorem and the continuum hypothesis

Abstract

Bibliographical note

Keywords

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