Regular ultrafilters and finite square principles

Juliette Kennedy*, Saharon Shelah, Jouko Väänänen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We show that many singular cardinals ë above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle □ λ,Dfin introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ/D is not λ++ -universal and elementarily equivalent models M and N of size λ for which M λ/D and Nλ/D are non-isomorphic. The question of the existence of such ultrafilters and models was raised in [I].

Original languageEnglish
Pages (from-to)817-823
Number of pages7
JournalJournal of Symbolic Logic
Volume73
Issue number3
DOIs
StatePublished - Sep 2008

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