Regular ultrafilters and finite square principles

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    Abstract

    We show that many singular cardinals lambda above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle square(fin)(lambda,D) introduced in [3]. For such ultrafilters D and cardinals lambda there are models of size lambda for which M-lambda/D is not lambda(++)-universal and elementarily equivalent models M and N of size lambda for which M-lambda/D and N-lambda/D are non-isomorphic. The question of the existence of such ultrafilters and models was raised in [1].
    Original languageEnglish
    JournalJournal of Symbolic Logic
    Volume73
    Issue number3
    Pages (from-to)817-823
    Number of pages7
    ISSN0022-4812
    DOIs
    Publication statusPublished - 2008
    MoE publication typeA1 Journal article-refereed

    Fields of Science

    • 111 Mathematics

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