14 found
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  1.  6
    A Groszek‐Laver Pair of Undistinguishable ‐Classes.Mohammad Golshani, Vladimir Kanovei & Vassily Lyubetsky - 2017 - Mathematical Logic Quarterly 63 (1-2):19-31.
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  2.  10
    The Tree Property at Double Successors of Singular Cardinals of Uncountable Cofinality.Mohammad Golshani & Rahman Mohammadpour - 2018 - Annals of Pure and Applied Logic 169 (2):164-175.
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  3.  9
    Collapsing the Cardinals of HOD.James Cummings, Sy David Friedman & Mohammad Golshani - 2015 - Journal of Mathematical Logic 15 (2):1550007.
    Assuming that GCH holds and [Formula: see text] is [Formula: see text]-supercompact, we construct a generic extension [Formula: see text] of [Formula: see text] in which [Formula: see text] remains strongly inaccessible and [Formula: see text] for every infinite cardinal [Formula: see text]. In particular the rank-initial segment [Formula: see text] is a model of ZFC in which [Formula: see text] for every infinite cardinal [Formula: see text].
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  4.  13
    The Special Aronszajn Tree Property.Mohammad Golshani & Yair Hayut - 2019 - Journal of Mathematical Logic 20 (1):2050003.
    Assuming the existence of a proper class of supercompact cardinals, we force a generic extension in which, for every regular cardinal [Formula: see text], there are [Formula: see text]-Aronszajn trees, and all such trees are special.
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  5.  21
    Shelah's Strong Covering Property and CH in V [R ].Esfandiar Eslami & Mohammad Golshani - 2012 - Mathematical Logic Quarterly 58 (3):153-158.
    In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of equation image by adding a real.
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  6.  1
    On Cuts in Ultraproducts of Linear Orders I.Mohammad Golshani & Saharon Shelah - 2016 - Journal of Mathematical Logic 16 (2):1650008.
    For an ultrafilter [Formula: see text] on a cardinal [Formula: see text] we wonder for which pair [Formula: see text] of regular cardinals, we have: for any [Formula: see text]-saturated dense linear order [Formula: see text] has a cut of cofinality [Formula: see text] We deal mainly with the case [Formula: see text].
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  7.  40
    Independence of Higher Kurepa Hypotheses.Sy-David Friedman & Mohammad Golshani - 2012 - Archive for Mathematical Logic 51 (5-6):621-633.
    We study the Generalized Kurepa hypothesis introduced by Chang. We show that relative to the existence of an inaccessible cardinal the Gap-n-Kurepa hypothesis does not follow from the Gap-m-Kurepa hypothesis for m different from n. The use of an inaccessible is necessary for this result.
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  8.  16
    The Tree Property at the Successor of a Singular Limit of Measurable Cardinals.Mohammad Golshani - 2018 - Archive for Mathematical Logic 57 (1-2):3-25.
    Assume \ is a singular limit of \ supercompact cardinals, where \ is a limit ordinal. We present two methods for arranging the tree property to hold at \ while making \ the successor of the limit of the first \ measurable cardinals. The first method is then used to get, from the same assumptions, the tree property at \ with the failure of SCH at \. This extends results of Neeman and Sinapova. The second method is also used to (...)
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  9.  13
    On a Question of Silver About Gap-Two Cardinal Transfer Principles.Mohammad Golshani & Shahram Mohsenipour - 2018 - Archive for Mathematical Logic 57 (1-2):27-35.
    Assuming the existence of a Mahlo cardinal, we produce a generic extension of Gödel’s constructible universe L, in which the \ holds and the transfer principles \ \rightarrow \) and \ \rightarrow \) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.
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  10.  14
    Hod, V and the Gch.Mohammad Golshani - 2017 - Journal of Symbolic Logic 82 (1):224-246.
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  11.  5
    Specializing Trees and Answer to a Question of Williams.Mohammad Golshani & Saharon Shelah - 2020 - Journal of Mathematical Logic 21 (1):2050023.
    We show that if [Formula: see text] then any nontrivial [Formula: see text]-closed forcing notion of size [Formula: see text] is forcing equivalent to [Formula: see text] the Cohen forcing for adding a new Cohen subset of [Formula: see text] We also produce, relative to the existence of suitable large cardinals, a model of [Formula: see text] in which [Formula: see text] and all [Formula: see text]-closed forcing notion of size [Formula: see text] collapse [Formula: see text] and hence are (...)
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  12.  7
    The Tree Property at Double Successors of Singular Cardinals of Uncountable Cofinality with Infinite Gaps.Mohammad Golshani & Alejandro Poveda - 2021 - Annals of Pure and Applied Logic 172 (1):102853.
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  13.  4
    On Cuts in Ultraproducts of Linear Orders II.Mohammad Golshani & Saharon Shelah - 2018 - Journal of Symbolic Logic 83 (1):29-39.
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  14.  2
    Killing the $GCH$ Everywhere with a Single Real.Sy-David Friedman & Mohammad Golshani - 2013 - Journal of Symbolic Logic 78 (3):803-823.
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