Between reduced powers and ultrapowers, II
Logic
2022-07-18 v4
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.
Keywords
Cite
@article{arxiv.2011.07352,
title = {Between reduced powers and ultrapowers, II},
author = {Ilijas Farah and Saharon Shelah},
journal= {arXiv preprint arXiv:2011.07352},
year = {2022}
}
Comments
31 pages. Minor changes, gory details added to the proof of Lemma 2.1. To appear in TAMS