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arXiv · 1712.06198

Ultrafilter extensions do not preserve elementary equivalence

Denis I. Saveliev·Saharon Shelah
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Abstract

We show that there exist models $\mathcal M_1$ and $\mathcal M_2$ such that $\mathcal M_1$ elementarily embeds into $\mathcal M_2$ but their ultrafilter extensions $\beta(\mathcal M_1)$ and $\beta(\mathcal M_2)$ are not elementarily equivalent.

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Denis I. Saveliev, Saharon Shelah. 2017-12-17. Ultrafilter extensions do not preserve elementary equivalence. https://arxiv.org/abs/1712.06198

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