The Keisler-Shelah isomorphism theorem and the continuum hypothesis II

2021/12/31 by Mohammad Golshani, Golshani, Mohammad, Saharon shelah +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2112.15468

openalex publication_date 2021/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue the investigation started in [Sh:1215] 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 \mathbf m=⟨ (\mathbbM¹_n, \mathbbM²_n: 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 \mathcal D on ω, if the ultraproducts ∏_{\mathcal D} \mathbbM¹_n and ∏_{\mathcal D} \mathbbM²_n are elementarily equivalent, then they are isomorphic.

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