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Menachem Magidor [61]M. Magidor [12]
  1.  6
    Nonmonotonic Reasoning, Preferential Models and Cumulative Logics.Sarit Kraus, Daniel Lehmann & Menachem Magidor - 1990 - Artificial Intelligence 44 (1-2):167-207.
  2.  35
    Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
    Since the work of Gödel and Cohen, which showed that Hilbert's First Problem was independent of the usual assumptions of mathematics, there have been a myriad of independence results in many areas of mathematics. These results have led to the systematic study of several combinatorial principles that have proven effective at settling many of the important independent statements. Among the most prominent of these are the principles diamond and square discovered by Jensen. Simultaneously, attempts have been made to find suitable (...)
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  3.  1
    What Does a Conditional Knowledge Base Entail?Daniel Lehmann & Menachem Magidor - 1992 - Artificial Intelligence 55 (1):1-60.
  4.  25
    How Large is the First Strongly Compact Cardinal? Or a Study on Identity Crises.Menachem Magidor - 1976 - Annals of Mathematical Logic 10 (1):33-57.
  5.  3
    What Does a Conditional Knowledge Base Entail?D. Lehmann & M. Magidor - 1994 - Artificial Intelligence 68 (2):411.
  6.  4
    Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
    Since the work of Gödel and Cohen, which showed that Hilbert's First Problem was independent of the usual assumptions of mathematics, there have been a myriad of independence results in many areas of mathematics. These results have led to the systematic study of several combinatorial principles that have proven effective at settling many of the important independent statements. Among the most prominent of these are the principles diamond and square discovered by Jensen. Simultaneously, attempts have been made to find suitable (...)
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  7.  51
    The Tree Property at Successors of Singular Cardinals.Menachem Magidor & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):385-404.
    Assuming some large cardinals, a model of ZFC is obtained in which $\aleph_{\omega+1}$ carries no Aronszajn trees. It is also shown that if $\lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees.
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  8.  33
    Large Cardinals and Definable Counterexamples to the Continuum Hypothesis.Matthew Foreman & Menachem Magidor - 1995 - Annals of Pure and Applied Logic 76 (1):47-97.
    In this paper we consider whether L(R) has “enough information” to contain a counterexample to the continuum hypothesis. We believe this question provides deep insight into the difficulties surrounding the continuum hypothesis. We show sufficient conditions for L(R) not to contain such a counterexample. Along the way we establish many results about nonstationary towers, non-reflecting stationary sets, generalizations of proper and semiproper forcing and Chang's conjecture.
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  9.  52
    Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
    We prove that the statement "For every pair A, B, stationary subsets of ω 2 , composed of points of cofinality ω, there exists an ordinal α such that both A ∩ α and $B \bigcap \alpha$ are stationary subsets of α" is equiconsistent with the existence of weakly compact cardinal. (This completes results of Baumgartner and Harrington and Shelah.) We also prove, assuming the existence of infinitely many supercompact cardinals, the statement "Every stationary subset of ω ω + 1 (...)
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  10.  52
    Distance Semantics for Belief Revision.Daniel Lehmann, Menachem Magidor & Karl Schlechta - 2001 - Journal of Symbolic Logic 66 (1):295-317.
    A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula α as the theory defined by the set of all those models of α that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates (...)
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  11.  35
    A Very Weak Square Principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
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  12.  14
    Shelah's Pcf Theory and its Applications.Maxim R. Burke & Menachem Magidor - 1990 - Annals of Pure and Applied Logic 50 (3):207-254.
    This is a survey paper giving a self-contained account of Shelah's theory of the pcf function pcf={cf:D is an ultrafilter on a}, where a is a set of regular cardinals such that a
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  13.  28
    Canonical Structure in the Universe of Set Theory: Part Two.James Cummings, Matthew Foreman & Menachem Magidor - 2006 - Annals of Pure and Applied Logic 142 (1):55-75.
    We prove a number of consistency results complementary to the ZFC results from our paper [J. Cummings, M. Foreman, M. Magidor, Canonical structure in the universe of set theory: part one, Annals of Pure and Applied Logic 129 211–243]. We produce examples of non-tightly stationary mutually stationary sequences, sequences of cardinals on which every sequence of sets is mutually stationary, and mutually stationary sequences not concentrating on a fixed cofinality. We also give an alternative proof for the consistency of the (...)
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  14.  24
    Canonical Structure in the Universe of Set Theory: Part One.James Cummings, Matthew Foreman & Menachem Magidor - 2004 - Annals of Pure and Applied Logic 129 (1-3):211-243.
    We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we prove a form of “singular cardinal compactness” for Jensen's square principle. We then study the relationship between internally approachable and tight structures, which parallels to a certain extent the relationship between good and approachable points. In particular we characterise the tight structures in terms of PCF theory and use our characterisation to prove (...)
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  15.  77
    An Ideal Game.F. Galvin, T. Jech & M. Magidor - 1978 - Journal of Symbolic Logic 43 (2):284-292.
  16. The Weak □* is Really Weaker Than the Full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
  17.  9
    Distance Semantics for Belief Revision.Daniel Lehmann, Menachem Magidor & Karl Schlechta - 2001 - Journal of Symbolic Logic 66 (1):295-317.
    A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula $\alpha$ as the theory defined by the set of all those models of $\alpha$ that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates (...)
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  18.  28
    The Number of Normal Measures.Sy-David Friedman & Menachem Magidor - 2009 - Journal of Symbolic Logic 74 (3):1069-1080.
    There have been numerous results showing that a measurable cardinal κ can carry exactly α normal measures in a model of GCH, where a is a cardinal at most κ⁺⁺. Starting with just one measurable cardinal, we have [9] (for α = 1), [10] (for α = κ⁺⁺, the maximum possible) and [1] (for α = κ⁺, after collapsing κ⁺⁺) . In addition, under stronger large cardinal hypotheses, one can handle the remaining cases: [12] (starting with a measurable cardinal of (...)
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  19.  9
    Omitting Types in Logic of Metric Structures.Ilijas Farah & Menachem Magidor - 2018 - Journal of Mathematical Logic 18 (2):1850006.
    This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete...
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  20.  11
    Inner Models From Extended Logics: Part 1.Juliette Kennedy, Menachem Magidor & Jouko Väänänen - 2020 - Journal of Mathematical Logic 21 (2):2150012.
    If we replace first-order logic by second-order logic in the original definition of Gödel’s inner model L, we obtain the inner model of hereditarily ordinal definable sets [33]. In this paper...
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  21.  21
    Precipitous Ideals.T. Jech, M. Magidor, W. Mitchell & K. Prikry - 1980 - Journal of Symbolic Logic 45 (1):1-8.
  22.  40
    Extender Based Forcings.Moti Gitik & Menachem Magidor - 1994 - Journal of Symbolic Logic 59 (2):445-460.
    The paper is a continuation of [The SCH revisited]. In § 1 we define a forcing with countably many nice systems. It is used, for example, to construct a model "GCH below κ, c f κ = ℵ0, and $2^\kappa > \kappa^{+\omega}$" from 0(κ) = κ+ω. In § 2 we define a triangle iteration and use it to construct a model satisfying "{μ ≤ λ∣ c f μ = ℵ0 and $pp(\mu) > \lambda\}$ is countable for some λ". The question (...)
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  23.  32
    On ${\omega _1}$-Strongly Compact Cardinals.Joan Bagaria & Menachem Magidor - 2014 - Journal of Symbolic Logic 79 (1):266-278.
  24.  13
    Destructibility of the Tree Property at ${\aleph _{\omega + 1}}$.Yair Hayut & Menachem Magidor - 2019 - Journal of Symbolic Logic 84 (2):621-631.
  25.  69
    On Löwenheim–Skolem–Tarski Numbers for Extensions of First Order Logic.Menachem Magidor & Jouko Väänänen - 2011 - Journal of Mathematical Logic 11 (1):87-113.
    We show that, assuming the consistency of a supercompact cardinal, the first inaccessible cardinal can satisfy a strong form of a Löwenheim–Skolem–Tarski theorem for the equicardinality logic L, a logic introduced in [5] strictly between first order logic and second order logic. On the other hand we show that in the light of present day inner model technology, nothing short of a supercompact cardinal suffices for this result. In particular, we show that the Löwenheim–Skolem–Tarski theorem for the equicardinality logic at (...)
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  26.  11
    Destructibility of the Tree Property at אω+1.Yair Hayut & Menachem Magidor - forthcoming - Journal of Symbolic Logic:1-10.
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  27.  73
    The Monadic Theory of Ω2.Yuri Gurevich, Menachem Magidor & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (2):387-398.
    Assume ZFC + "There is a weakly compact cardinal" is consistent. Then: (i) For every $S \subseteq \omega, \mathrm{ZFC} +$ "S and the monadic theory of ω 2 are recursive each in the other" is consistent; and (ii) ZFC + "The full second-order theory of ω 2 is interpretable in the monadic theory of ω 2 " is consistent.
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  28.  34
    The Consistency Strength of Successive Cardinals with the Tree Property.Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (4):1837-1847.
    If ω n has the tree property for all $2 \leq n and $2^{ , then for all X ∈ H ℵ ω and $n exists.
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  29.  11
    The Eightfold Way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.
    Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing that any of their eight Boolean combinations can be forced to hold at${\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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  30.  21
    The Non-Compactness of Square.James Cummings, Matthew Foreman & Menachem Magidor - 2003 - Journal of Symbolic Logic 68 (2):637-643.
  31.  18
    Chang's Conjecture and Powers of Singular Cardinals.Menachem Magidor - 1977 - Journal of Symbolic Logic 42 (2):272-276.
  32.  18
    Reflection of Stationary Sets and the Tree Property at the Successor of a Singular Cardinal.Laura Fontanella & Menachem Magidor - 2017 - Journal of Symbolic Logic 82 (1):272-291.
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  33.  11
    Instances of Dependent Choice and the Measurability of ℵω + 1.Arthur W. Apter & Menachem Magidor - 1995 - Annals of Pure and Applied Logic 74 (3):203-219.
    Starting from cardinals κ κ is measurable, we construct a model for the theory “ZF + n < ω[DCn] + ω + 1 is a measurable cardinal”. This is the maximum amount of dependent choice consistent with the measurability of ω + 1, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible.
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  34.  20
    On Supercompactness and the Continuum Function.Brent Cody & Menachem Magidor - 2014 - Annals of Pure and Applied Logic 165 (2):620-630.
    Given a cardinal κ that is λ-supercompact for some regular cardinal λ⩾κ and assuming GCH, we show that one can force the continuum function to agree with any function F:[κ,λ]∩REG→CARD satisfying ∀α,β∈domα F. Our argument extends Woodinʼs technique of surgically modifying a generic filter to a new case: Woodinʼs key lemma applies when modifications are done on the range of j, whereas our argument uses a new key lemma to handle modifications done off of the range of j on the (...)
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  35. Berardi, S., see Barbanera, F.M. Ferrari, P. Miglioli, M. Foreman, M. Magidor, T. Huuskonen, R. Sommer, J. von Plato & J. Zapletal - 1995 - Annals of Pure and Applied Logic 76:303.
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  36.  21
    Some Highly Undecidable Lattices.Menachem Magidor, John W. Rosenthal, Mattiyahu Rubin & Gabriel Srour - 1990 - Annals of Pure and Applied Logic 46 (1):41-63.
  37.  21
    Jack H. Silver. Measurable Cardinals and Well-Orderings. Annals of Mathematics, Ser. 2 Vol. 94 , Pp. 414–446.Menachem Magidor - 1974 - Journal of Symbolic Logic 39 (2):330-331.
  38.  17
    The Consistency Strength of Hyperstationarity.Joan Bagaria, Menachem Magidor & Salvador Mancilla - 2019 - Journal of Mathematical Logic 20 (1):2050004.
    We introduce the large-cardinal notions of ξ-greatly-Mahlo and ξ-reflection cardinals and prove (1) in the constructible universe, L, the first ξ-reflection cardinal, for ξ a successor ordinal, is strictly between the first ξ-greatly-Mahlo and the first Π1ξ-indescribable cardinals, (2) assuming the existence of a ξ-reflection cardinal κ in L, ξ a successor ordinal, there exists a forcing notion in L that preserves cardinals and forces that κ is (ξ+1)-stationary, which implies that the consistency strength of the existence of a (ξ+1)-stationary (...)
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  39. Master Index to Volumes 71-80.K. A. Abrahamson, R. G. Downey, M. R. Fellows, A. W. Apter, M. Magidor, M. I. da ArchangelskyDekhtyar, M. A. Taitslin, M. A. Arslanov & S. Lempp - 1996 - Annals of Pure and Applied Logic 80:293-298.
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  40. Ignjatovik, A., See Buss, SR.A. W. Apter, M. Magidor, Ch Cornaros & K. Hauser - 1995 - Annals of Pure and Applied Logic 74:297.
     
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  41. Extender Based Forcings.Moti Gitik, Menachem Magidor & William J. Mitchell - 2003 - Bulletin of Symbolic Logic 9 (2):237-241.
     
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  42. Subcompact Cardinals, Type Omission, and Ladder Systems.Yair Hayut & Menachem Magidor - 2022 - Journal of Symbolic Logic 87 (3):1111-1129.
    We provide a model theoretical and tree property-like characterization of $\lambda $ - $\Pi ^1_1$ -subcompactness and supercompactness. We explore the behavior of these combinatorial principles at accessible cardinals.
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  43.  8
    Identity Crisis Between Supercompactness and Vǒpenka’s Principle.Yair Hayut, Menachem Magidor & Alejandro Poveda - 2022 - Journal of Symbolic Logic 87 (2):626-648.
    In this paper we study the notion of $C^{}$ -supercompactness introduced by Bagaria in [3] and prove the identity crises phenomenon for such class. Specifically, we show that consistently the least supercompact is strictly below the least $C^{}$ -supercompact but also that the least supercompact is $C^{}$ -supercompact }$ -supercompact). Furthermore, we prove that under suitable hypothesis the ultimate identity crises is also possible. These results solve several questions posed by Bagaria and Tsaprounis.
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  44. On the Standard Part of Nonstandard Models of Set Theory.Menachem Magidor, Saharon Shelah & Jonathan Stavi - 1983 - Journal of Symbolic Logic 48 (1):33-38.
    We characterize the ordinals α of uncountable cofinality such that α is the standard part of a nonstandard model of ZFC (or equivalently KP).
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  45.  44
    Book Reviews. [REVIEW]Baruch Brody, R. G. Swinburne, Alex C. Michalos, Gershon Weiler, Geoffrey Sampson, Marcelo Dascal, Shalom Lappin, Yehuda Melzer, Joseph Horovitz, Haim Marantz, Marcelo Dascal, M. Magidor & Michael Katz - 1974 - Philosophia 4 (2-3):279-281.
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  46.  20
    Compactness and Transfer for a Fragment of L 2.M. Magidor & J. Malitz - 1977 - Journal of Symbolic Logic 42 (2):261-268.
  47.  22
    $0^Sharp$ and Some Forcing Principles. [REVIEW]Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39-46.
  48.  27
    The Independence of Δ1n.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350 - 362.
    In this paper we prove the independence of δ 1 n for n ≥ 3. We show that δ 1 4 can be forced to be above any ordinal of L using set forcing. For δ 1 3 we prove that it can be forced, using set forcing, to be above any L cardinal κ such that κ is Π 1 definable without parameters in L. We then show that δ 1 3 cannot be forced by a set forcing to (...)
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  49.  11
    On the Spectrum of Characters of Ultrafilters.Shimon Garti, Menachem Magidor & Saharon Shelah - 2018 - Notre Dame Journal of Formal Logic 59 (3):371-379.
    We show that the character spectrum Spχ may include any prescribed set of regular cardinals between λ and 2λ.
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  50.  25
    Two Weak Consequences of 0#. [REVIEW]M. Gitik, M. Magidor & H. Woodin - 1985 - Journal of Symbolic Logic 50 (3):597 - 603.
    It is proven that the following statement: "there exists a club $C \subseteq \kappa$ such that every α ∈ C is an inaccessible cardinal in L and, for every δ a limit point of C, C ∩ δ is almost contained in every club of δ of L" is equiconsistent with a weakly compact cardinal if κ = ℵ 1 , and with a weakly compact cardinal of order 1 if κ = ℵ 2.
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