Academic Journal
Saturation of reduced products.
| Τίτλος: | Saturation of reduced products. |
|---|---|
| Συγγραφείς: | De Bondt, Ben1,2 (AUTHOR) bdebondt@uni-muenster.de, Farah, Ilijas3,4 (AUTHOR) ifarah@yorku.ca, Vignati, Alessandro1 (AUTHOR) vignati@imj-prg.fr |
| Πηγή: | Journal of Mathematical Logic. Feb2026, p1. 31p. |
| Θεματικοί όροι: | *Model theory, *Continuum hypothesis |
| Περίληψη: | In this paper, we study reduced products M =∏nMn/Fin of countable structures in a countable language associated with the Fréchet ideal. We prove that such M is 2ℵ0-saturated if its theory is stable and not ℵ2-saturated otherwise (regardless of whether the Continuum Hypothesis holds). This implies that M is isomorphic to an ultrapower (associated with an ultrafilter on ℕ) if its theory is stable, even if the CH fails. We also improve a result of Farah and Shelah and prove that there is a forcing extension in which such reduced product M is isomorphic to an ultrapower if and only if the theory of M is stable. All of these conclusions apply for reduced products associated with Fσ ideals or more general layered ideals. We also prove that a reduced product associated with the asymptotic density zero ideal 풵0, or any other analytic P-ideal that is not Fσ, is not even ℵ1-saturated if its theory is unstable. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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