6 found
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  1.  26
    Some Results About (+) Proved by Iterated Forcing.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):515-531.
    We shall show the consistency of CH+ᄀ(+) and CH+(+)+ there are no club guessing sequences on ω₁. We shall also prove that ◊⁺ does not imply the existence of a strong club guessing sequence ω₁.
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  2.  9
    The Comparison of Various Club Guessing Principles.Tetsuya Ishiu - 2015 - Annals of Pure and Applied Logic 166 (5):583-600.
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  3.  11
    Club Guessing Sequences and Filters.Tetsuya Ishiu - 2005 - Journal of Symbolic Logic 70 (4):1037-1071.
    We investigate club guessing sequences and filters. We prove that assuming V=L, there exists a strong club guessing sequence on μ if and only if μ is not ineffable for every uncountable regular cardinal μ. We also prove that for every uncountable regular cardinal μ, relative to the existence of a Woodin cardinal above μ, it is consistent that every tail club guessing ideal on μ is precipitous.
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  4.  36
    ℙmax Variations for Separating Club Guessing Principles.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):532-544.
    In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω | . It was shown in [1] that (...)
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  5.  8
    The Saturation of Club Guessing Ideals.Tetsuya Ishiu - 2006 - Annals of Pure and Applied Logic 142 (1):398-424.
    We prove that it is consistent that there exists a saturated tail club guessing ideal on ω1 which is not a restriction of the non-stationary ideal. Two proofs are presented. The first one uses a new forcing axiom whose consistency can be proved from a supercompact cardinal. The resulting model can satisfy either CH or 20=2. The second one is a direct proof from a Woodin cardinal, which gives a witnessing model with CH.
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  6.  7
    A Tail Club Guessing Ideal Can Be Saturated Without Being a Restriction of the Nonstationary Ideal.Tetsuya Ishiu - 2005 - Notre Dame Journal of Formal Logic 46 (3):327-333.
    We outline the proof of the consistency that there exists a saturated tail club guessing ideal on ω₁ which is not a restriction of the nonstationary ideal. A new class of forcing notions and the forcing axiom for the class are introduced for this purpose.
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