Between reduced powers and ultrapowers, II

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.

31 pages. Minor changes, gory details added to the proof of Lemma 2.1. To appear in TAMS