18 found
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  1.  10
    Varsovian Models I.Grigor Sargsyan & Ralf Schindler - 2018 - Journal of Symbolic Logic 83 (2):496-528.
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  2.  44
    Descriptive Inner Model Theory.Grigor Sargsyan - 2013 - Bulletin of Symbolic Logic 19 (1):1-55.
    The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture. One particular motivation for resolving MSC is that (...)
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  3.  18
    Nontame Mouse From the Failure of Square at a Singular Strong Limit Cardinal.Grigor Sargsyan - 2014 - Journal of Mathematical Logic 14 (1):1450003.
    Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216 89–117] and Steel [PFA implies AD L, J. Symbolic Logic70 1255–1296], we show that the failure of square principle at a singular strong limit cardinal implies that there is a nontame mouse. The proof presented is the first inductive step beyond L of the core model induction that is aimed at getting a model of ADℝ + "Θ is regular" from the failure of square at a singular strong (...)
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  4.  46
    On HOD-Supercompactness.Grigor Sargsyan - 2008 - Archive for Mathematical Logic 47 (7-8):765-768.
    During his Fall 2005 set theory seminar, Woodin asked whether V-supercompactness implies HOD-supercompactness. We show, as he predicted, that that the answer is no.
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  5.  37
    Indestructible Strong Compactness but Not Supercompactness.Arthur W. Apter, Moti Gitik & Grigor Sargsyan - 2012 - Annals of Pure and Applied Logic 163 (9):1237-1242.
  6.  37
    Identity Crises and Strong Compactness III: Woodin Cardinals. [REVIEW]Arthur W. Apter & Grigor Sargsyan - 2005 - Archive for Mathematical Logic 45 (3):307-322.
    We show that it is consistent, relative to n ∈ ω supercompact cardinals, for the strongly compact and measurable Woodin cardinals to coincide precisely. In particular, it is consistent for the first n strongly compact cardinals to be the first n measurable Woodin cardinals, with no cardinal above the n th strongly compact cardinal being measurable. In addition, we show that it is consistent, relative to a proper class of supercompact cardinals, for the strongly compact cardinals and the cardinals which (...)
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  7.  34
    An Equiconsistency for Universal Indestructibility.Arthur W. Apter & Grigor Sargsyan - 2010 - Journal of Symbolic Logic 75 (1):314-322.
    We obtain an equiconsistency for a weak form of universal indestructibility for strongness. The equiconsistency is relative to a cardinal weaker in consistency strength than a Woodin cardinal. Stewart Baldwin's notion of hyperstrong cardinal. We also briefly indicate how our methods are applicable to universal indestructibility for supercompactness and strong compactness.
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  8.  29
    On the Indestructibility Aspects of Identity Crisis.Grigor Sargsyan - 2009 - Archive for Mathematical Logic 48 (6):493-513.
    We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi–Magidor theorem from (in The independence between the concepts of compactness and supercompactness, circulated manuscript), i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact cardinals can be the first n measurable cardinals while the strong (...)
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  9.  7
    The Mouse Set Conjecture for Sets of Reals.Grigor Sargsyan & John Steel - 2015 - Journal of Symbolic Logic 80 (2):671-683.
  10.  9
    An inner model theoretic proof of Becker’s theorem.Grigor Sargsyan - 2019 - Archive for Mathematical Logic 58 (7):999-1003.
    We re-prove Becker’s theorem from Becker :229–234, 1981) by showing that \}\) implies that \\vDash ``\omega _2\) is -supercompact”. Our proof uses inner model theoretic tools instead of Baire category. We also show that \ is \-strongly compact.
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  11.  10
    Universal Indestructibility for Degrees of Supercompactness and Strongly Compact Cardinals.Arthur W. Apter & Grigor Sargsyan - 2008 - Archive for Mathematical Logic 47 (2):133-142.
    We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness. In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly compact cardinals, each of which exhibits a significant amount of indestructibility (...)
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  12.  5
    Derived Models of Mice Below the Least Fixpoint of the Solovay Sequence.Dominik Adolf & Grigor Sargsyan - 2019 - Journal of Symbolic Logic 84 (1):27-53.
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  13.  5
    Wadge Degrees and Projective Ordinals. The Cabal Seminar, Volume II, Edited by A. S. Kechris, B. Löwe, and J.R. Steel, Lecture Notes in Logic, Vol. 37. Association for Symbolic Logic and Cambridge University Press, Cambridge, 2012, Xxii + 526 Pp. [REVIEW]Grigor Sargsyan - 2013 - Bulletin of Symbolic Logic 19 (4):492-496.
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  14.  7
    Hod Up to ADR+Θ is Measurable.Rachid Atmai & Grigor Sargsyan - 2019 - Annals of Pure and Applied Logic 170 (1):95-108.
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  15.  2
    Tame Failures of the Unique Branch Hypothesis and Models of ADℝ + Θ is Regular.Grigor Sargsyan & Nam Trang - 2016 - Journal of Mathematical Logic 16 (2):1650007.
    In this paper, we show that the failure of the unique branch hypothesis for tame iteration trees implies that in some homogenous generic extension of [Formula: see text] there is a transitive model [Formula: see text] containing [Formula: see text] such that [Formula: see text] is regular. The results of this paper significantly extend earlier works from [Non-tame mice from tame failures of the unique branch bypothesis, Canadian J. Math. 66 903–923; Core models with more Woodin cardinals, J. Symbolic Logic (...)
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  16.  19
    Madison, WI, USA March 31–April 3, 2012.Alan Dow, Isaac Goldbring, Warren Goldfarb, Joseph Miller, Toniann Pitassi, Antonio Montalbán, Grigor Sargsyan, Sergei Starchenko & Moshe Vardi - 2013 - Bulletin of Symbolic Logic 19 (2).
  17.  7
    On the Prewellorderings Associated with the Directed Systems of Mice.Grigor Sargsyan - 2013 - Journal of Symbolic Logic 78 (3):735-763.
  18.  7
    An Inner Model Proof of the Strong Partition Property for $Delta^{2}_{1}$.Grigor Sargsyan - 2014 - Notre Dame Journal of Formal Logic 55 (4):563-568.
    Assuming $V=L+AD$, using methods from inner model theory, we give a new proof of the strong partition property for ${\sim}{ \delta }^{2}_{1}$. The result was originally proved by Kechris et al.
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