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  1. The Nonstationary Ideal in the Pmax Extension.Paul B. Larson - 2007 - Journal of Symbolic Logic 72 (1):138 - 158.
    The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.
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  • The entire NS ideal on pγ μ can be precipitous.Noa Goldring - 1997 - Journal of Symbolic Logic 62 (4):1161 - 1172.
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  • Ideals and combinatorial principles.Douglas Burke & Yo Matsubara - 1997 - Journal of Symbolic Logic 62 (1):117-122.
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  • 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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  • 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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  • Local weak presaturation of the strongly non‐stationary ideal.Masahiro Shioya & Naoki Yamaura - 2020 - Mathematical Logic Quarterly 66 (1):99-103.
    We give a model of set theory in which the strongly non‐stationary ideal over is weakly presaturated below some canonical set. Here μ is a regular uncountable cardinal. The model is the forcing extension with the Lévy collapse of a Woodin cardinal to the successor of μ. This improves on results of Goldring and of the first author.
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