More on regular reduced products

Juliette Cara Kennedy*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The authors show, by means of a finitary version □ λ.Dfin of the combinatorial principle □λb* of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size <λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. If in addition 2λ = λ+ and i < λ implies |Mi| + |Ni| ≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].

Original languageEnglish
Pages (from-to)1261-1266
Number of pages6
JournalJournal of Symbolic Logic
Volume69
Issue number4
DOIs
StatePublished - Dec 2004

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