New combinatorial principle on singular cardinals and normal ideals

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    Abstract

    We introduce a new combinatorial principle on singular cardinals. This principle allows us to take a kind of a diagonal intersection of more than λ many measure one sets of certain normal ideals over ℘(λ). Under the principle, we give various characterizations of the saturation property of normal ideals over ℘(λ). We also consider Chang's type transfer properties under the principle, and, when λ is Jónsson, we prove that every normal ideal over ℘(λ) with {x ⊆ λ : |x| = λ} measure one cannot have strong properties.

    Original languageEnglish
    JournalMathematical Logic Quarterly
    DOIs
    Publication statusAccepted/In press - 2018 Jan 1

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    Saturation
    Intersection

    ASJC Scopus subject areas

    • Logic

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