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.
Original language | English |
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Pages (from-to) | 9007-9034 |
Number of pages | 28 |
Journal | Transactions of the American Mathematical Society |
Volume | 375 |
Issue number | 12 |
DOIs | |
State | Published - Dec 2022 |
Bibliographical note
Publisher Copyright:© 2022 American Mathematical Society.
Keywords
- Cohen model
- Continuum Hypothesis
- Proper Forcing Axiom
- reduced powers
- saturated models
- small basis
- Ultrapowers
- universal models