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 |
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Pages (from-to) | 789-801 |
Number of pages | 13 |
Journal | Monatshefte fur Mathematik |
Volume | 201 |
Issue number | 3 |
DOIs | |
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 continuum hypothesis
- The Keisler-Shelah isomorphism theorem
- Ultraproduct