Between reduced powers and ultrapowers, II

Ilijas Farah; Saharon Shelah

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arXiv · 2011.07352

Between reduced powers and ultrapowers, II

Ilijas Farah·Saharon Shelah

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Abstract

We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fr\'echet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

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Ilijas Farah, Saharon Shelah. 2020-11-14. Between reduced powers and ultrapowers, II. https://arxiv.org/abs/2011.07352

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