# Sh:1223

- Golshani, M., & Shelah, S.
*The Keisler-Shelah isomorphism theorem and the continuum hypothesis II*. Monatshefte Fur Mathematik. To appear. arXiv: 2112.15468 -
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 \langle (\mathbb{M}^{1}_n, \mathbb{M}^{2}_n: n < \omega \rangle of models of size at most \aleph_1 in a countable language, if the sequence satisfies a mild extra property, then for every non-principal ultrafilter \mathcal D on \omega, if the ultraproducts \prod\limits_{\mathcal D} \mathbb{M}^{1}_n and \prod\limits_{\mathcal D} \mathbb{M}^{2}_n are elementarily equivalent, then they are isomorphic. - Version 2022-08-30_2 (16p)

Bib entry

@article{Sh:1223, author = {Golshani, Mohammad and Shelah, Saharon}, title = {{The Keisler-Shelah isomorphism theorem and the continuum hypothesis II}}, journal = {Monatshefte fur Mathematik}, year = {to appear}, note = {\href{https://arxiv.org/abs/2112.15468}{arXiv: 2112.15468}}, arxiv_number = {2112.15468} }