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  1.  17
    The Cardinal Coefficients of the Ideal $${{\Mathcal {I}}_{F}}$$.Noboru Osuga & Shizuo Kamo - 2008 - Archive for Mathematical Logic 47 (7-8):653-671.
    In 2002, Yorioka introduced the σ-ideal ${{\mathcal {I}}_f}$ for strictly increasing functions f from ω into ω to analyze the cofinality of the strong measure zero ideal. For each f, we study the cardinal coefficients (the additivity, covering number, uniformity and cofinality) of ${{\mathcal {I}}_f}$.
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  2.  10
    Many Different Covering Numbers of Yorioka’s Ideals.Noboru Osuga & Shizuo Kamo - 2014 - Archive for Mathematical Logic 53 (1-2):43-56.
    For ${b \in {^{\omega}}{\omega}}$ , let ${\mathfrak{c}^{\exists}_{b, 1}}$ be the minimal number of functions (or slaloms with width 1) to catch every functions below b in infinitely many positions. In this paper, by using the technique of forcing, we construct a generic model in which there are many coefficients ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ with pairwise different values. In particular, under the assumption that a weakly inaccessible cardinal exists, we can construct a generic model in which there are continuum many coefficients ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ (...)
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  3.  16
    Nonstandard Natural Number Systems and Nonstandard Models.Shizuo Kamo - 1981 - Journal of Symbolic Logic 46 (2):365-376.
    It is known (see [1, 3.1.5]) that the order type of the nonstandard natural number system * N has the form ω + (ω * + ω) θ, where θ is a dense order type without first or last element and ω is the order type of N. Concerning this, Zakon [2] examined * N more closely and investigated the nonstandard real number system * R, as an ordered set, as an additive group and as a uniform space. He raised (...)
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