11 found
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  1.  16
    The Tree Property and the Failure of the Singular Cardinal Hypothesis at ℵω2.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (3):934-946.
    We show that given ù many supercompact cardinals, there is a generic extension in which the tree property holds at ℵ ω²+1 and the SCH fails at ℵ ω².
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  2.  8
    Combinatorics Atℵω.Dima Sinapova & Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (4):996-1007.
    We construct a model in which the singular cardinal hypothesis fails at ℵωℵω. We use characterizations of genericity to show the existence of a projection between different Prikry type forcings.
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  3.  12
    The Tree Property at And.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.
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  4.  12
    The Tree Property at ℵ Ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
    We show that given ω many supercompact cardinals, there is a generic extension in which there are no Aronszajn trees at ℵω+1. This is an improvement of the large cardinal assumptions. The previous hypothesis was a huge cardinal and ω many supercompact cardinals above it, in Magidor—Shelah [7].
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  5.  13
    A Model for a Very Good Scale and a Bad Scale.Dima Sinapova - 2008 - Journal of Symbolic Logic 73 (4):1361-1372.
    Given a supercompact cardinal κ and a regular cardinal Λ < κ, we describe a type of forcing such that in the generic extension the cofinality of κ is Λ, there is a very good scale at κ, a bad scale at κ, and SCH at κ fails. When creating our model we have great freedom in assigning the value of 2κ, and so we can make SCH hold or fail arbitrarily badly.
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  6.  2
    Kurepa trees and spectra of $${mathcal {L}}{omega 1,omega }$$Lω1,ω -sentences.Dima Sinapova & Ioannis Souldatos - forthcoming - Archive for Mathematical Logic:1-18.
    We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a single\-sentence \ that codes Kurepa trees to prove the following statements: The spectrum of \ is consistently equal to \ and also consistently equal to \\), where \ is weakly inaccessible.The amalgamation spectrum of \ is consistently equal to \ and \\), where again \ is weakly inaccessible. This is the first example of an \-sentence whose spectrum and amalgamation spectrum are consistently both right-open and right-closed. (...)
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  7.  44
    The Tree Property and the Failure of SCH at Uncountable Cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
    Given a regular cardinal λ and λ many supercompact cardinals, we describe a type of forcing such that in the generic extension there is a cardinal κ with cofinality λ, the Singular Cardinal Hypothesis at κ fails, and the tree property holds at κ +.
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  8.  16
    Itp, Isp, and Sch.Sherwood Hachtman & Dima Sinapova - 2019 - Journal of Symbolic Logic 84 (2):713-725.
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  9.  53
    A Cardinal Preserving Extension Making the Set of Points of Countable V Cofinality Nonstationary.Moti Gitik, Itay Neeman & Dima Sinapova - 2007 - Archive for Mathematical Logic 46 (5-6):451-456.
    Assuming large cardinals we produce a forcing extension of V which preserves cardinals, does not add reals, and makes the set of points of countable V cofinality in κ+ nonstationary. Continuing to force further, we obtain an extension in which the set of points of countable V cofinality in ν is nonstationary for every regular ν ≥ κ+. Finally we show that our large cardinal assumption is optimal.
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  10.  10
    The Eightfold Way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.
    Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing that any of their eight Boolean combinations can be forced to hold at${\kappa ^{ + + }}$, assuming that$\kappa = {\kappa ^{ < \kappa }}$and there is a weakly compact cardinal aboveκ.If in additionκis supercompact then we can forceκto be${\aleph _\omega }$in the extension. The proofs combine the techniques of adding and then destroying (...)
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  11.  8
    Itay Neeman. Forcing with Sequences of Models of Two Types. Notre Dame Journal of Formal Logic, Vol. 55 , Pp. 265–298.Dima Sinapova - 2015 - Bulletin of Symbolic Logic 21 (3):339-341.