Ultrafilter extensions do not preserve elementary equivalence

Published 17 Dec 2017 in math.LO | (1712.06198v2)

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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