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Between reduced powers and ultrapowers, II

2020/11/14 by Ilijas Farah, Saharon Shelah, Farah, Ilijas +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2011.07352

openalex publication_date 2020/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Fréchet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

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