• DOI:10.4064/fm198-5-2022
• Corpus ID: 236956543

The Keisler–Shelah isomorphism theorem and the continuum hypothesis II

@article{Golshani2021TheKI,
  title={The Keisler–Shelah isomorphism theorem and the continuum hypothesis II},
  author={Mohammad Golshani and Saharon Shelah},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2021},
  pages={1-13}
}

• M. Golshani, S. Shelah
• Published 9 August 2021
• Mathematics
• Monatshefte für Mathematik

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 $$\textbf{m}=\langle ({\mathbb {M}}^{1}_n, {\mathbb {M}}^{2}_n): n < \omega \rangle $$ m = ⟨ ( M n 1 , M n 2 ) : n < ω ⟩ of models of size at most $$\aleph _1$$ ℵ 1 in a countable language, if the sequence satisfies a mild extra property, then for every non-principal ultrafilter $$\mathcal D$$ D on $$\omega $$ ω , if the ultraproducts $$\prod \nolimits _{\mathcal D} {\mathbb {M}}^{1}_n$$ ∏ D M n 1 and $$\prod \nolimits _{\mathcal D} {\mathbb {M}}^{2}_n$$ ∏ D M n 2 are elementarily equivalent, then they are isomorphic.