6 found
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  1.  21
    Kurepa Trees and Namba Forcing.Bernhard König & Yasuo Yoshinobu - 2012 - Journal of Symbolic Logic 77 (4):1281-1290.
    We show that strongly compact cardinals and MM are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding ‘regressive' $\lambda$-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.
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  2.  18
    Operations, Climbability and the Proper Forcing Axiom.Yasuo Yoshinobu - 2013 - Annals of Pure and Applied Logic 164 (7-8):749-762.
    In this paper we show that the Proper Forcing Axiom is preserved under forcing over any poset PP with the following property: In the generalized Banach–Mazur game over PP of length , Player II has a winning strategy which depends only on the current position and the ordinal indicating the number of moves made so far. By the current position we mean: The move just made by Player I for a successor stage, or the infimum of all the moves made (...)
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  3.  39
    Approachability and Games on Posets.Yasuo Yoshinobu - 2003 - Journal of Symbolic Logic 68 (2):589-606.
    We show that for any infinite cardinal κ, every strongly $(\kappa + 1)-strategically$ closed poset is strongly $\kappa^+-strategically$ closed if and only if $AP_\kappa$ (the approachability property) holds, answering the question asked in [5]. We also give a complete classification of strengths of strategic closure properties and that of strong strategic closure properties respectively.
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  4.  27
    Dense Non-Reflection for Stationary Collections of Countable Sets.David Asperó, John Krueger & Yasuo Yoshinobu - 2010 - Annals of Pure and Applied Logic 161 (1):94-108.
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  5.  23
    The ⁎-Variation of the Banach–Mazur Game and Forcing Axioms.Yasuo Yoshinobu - 2017 - Annals of Pure and Applied Logic 168 (6):1335-1359.
  6.  11
    Σ-Short Boolean Algebras.Makoto Takahashi & Yasuo Yoshinobu - 2003 - Mathematical Logic Quarterly 49 (6):543-549.
    We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach-Mazur Boolean game. A σ-short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length ω does not have a nonzero lower bound. We give a characterization of σ-short Boolean algebras and study properties of σ-short Boolean algebras.
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