On regular reduced products
| dc.creator | Kennedy, Juliette | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2001-05-16 | |
| dc.date.accessioned | 2026-07-07T04:41:44Z | |
| dc.date.available | 2026-07-07T04:41:44Z | |
| dc.description | Assume <aleph_0,aleph_1>-><lambda,lambda^+>. Assume M is a model of a first order theory T of cardinality at most lambda^+ in a vocabulary L(T) of cardinality <= lambda . Let N be a model with the same vocabulary. Let Delta be a set of first order formulas in L(T) and let D be a regular filter on lambda. Then M is Delta-embeddable into the reduced power N^lambda/D, provided that every Delta-existential formula true in M is true also in N. We obtain the following corollary: for M as above and D a regular ultrafilter over lambda, M^lambda/D is lambda^{++}-universal. Our second result is as follows: For i<mu let M_i and N_i be elementarily equivalent models of a vocabulary which has has cardinality <=lambda. Suppose D is a regular filter on mu and <aleph_0,aleph_1>-><lambda,lambda^+> holds. We show that then the second player has a winning strategy in the Ehrenfeucht-Fraisse game of length lambda^+ on prod_i M_i/D and prod_i N_i/D. This yields the following corollary: Assume GCH and lambda regular). For L, M_i and N_i as above, if D is a regular filter on lambda, then prod_i M_i/D cong prod_i N_i/D . | |
| dc.identifier | https://arxiv.org/abs/math/0105135 | |
| dc.identifier | http://arxiv.org/abs/math/0105135 | |
| dc.identifier | J. Symbolic Logic 67 No. 3 (2002) 1169--1177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61480 | |
| dc.subject | Logic | |
| dc.title | On regular reduced products | |
| dc.type | text |