New combinatorial principle on singular cardinals and normal ideals

Toshimichi Usuba

    Research output: Contribution to journal › Article

    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

    Fingerprint

    Saturation
    Intersection

    ASJC Scopus subject areas

    • Logic

    Cite this

    New combinatorial principle on singular cardinals and normal ideals. / Usuba, Toshimichi.

    In: Mathematical Logic Quarterly, 01.01.2018.

    Research output: Contribution to journal › Article

    Usuba, T 2018, 'New combinatorial principle on singular cardinals and normal ideals', Mathematical Logic Quarterly. https://doi.org/10.1002/malq.201700024
    Usuba T. New combinatorial principle on singular cardinals and normal ideals. Mathematical Logic Quarterly. 2018 Jan 1. https://doi.org/10.1002/malq.201700024
    Usuba, Toshimichi. / New combinatorial principle on singular cardinals and normal ideals. In: Mathematical Logic Quarterly. 2018.
    @article{6bf7a4691c51438e9e2669da6d305435,
    title = "New combinatorial principle on singular cardinals and normal ideals",
    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 J{\'o}nsson, we prove that every normal ideal over ℘(λ) with {x ⊆ λ : |x| = λ} measure one cannot have strong properties.",
    author = "Toshimichi Usuba",
    year = "2018",
    month = "1",
    day = "1",
    doi = "10.1002/malq.201700024",
    language = "English",
    journal = "Mathematical Logic Quarterly",
    issn = "0942-5616",
    publisher = "Wiley-VCH Verlag",

    }

    TY - JOUR

    T1 - New combinatorial principle on singular cardinals and normal ideals

    AU - Usuba, Toshimichi

    PY - 2018/1/1

    Y1 - 2018/1/1

    N2 - 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.

    AB - 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.

    UR - http://www.scopus.com/inward/record.url?scp=85055553537&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85055553537&partnerID=8YFLogxK

    U2 - 10.1002/malq.201700024

    DO - 10.1002/malq.201700024

    M3 - Article

    JO - Mathematical Logic Quarterly

    JF - Mathematical Logic Quarterly

    SN - 0942-5616

    ER -

    Access to Document