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arXiv · 2108.03977

The Keisler-Shelah isomorphism theorem and the continuum hypothesis

Mohammad Golshani·Saharon Shelah
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Abstract

We show that if for any two elementary equivalent structures $\mathbf{M}, \mathbf{N}$ of size at most continuum in a countable language, $\mathbf{M}^{\omega}/ \mathcal{U} \simeq \mathbf{N}^\omega / \mathcal{U}$ for some ultrafilter $\mathcal{U}$ on $\omega,$ then $CH$ holds. We also provide some consistency results about Keisler and Shelah isomorphism theorems in the absence of $CH$.

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Mohammad Golshani, Saharon Shelah. 2021-08-09. The Keisler-Shelah isomorphism theorem and the continuum hypothesis. https://arxiv.org/abs/2108.03977

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