46 found
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  1.  27
    Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
  2.  12
    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 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 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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  3.  26
    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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  4.  9
    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.  19
    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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  6.  9
    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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  7.  6
    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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  8.  9
    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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  9.  20
    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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  10.  20
    A Very Weak Square Principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
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  11. The Weak □* is Really Weaker Than the Full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
  12.  45
    On Löwenheim–Skolem–Tarski Numbers for Extensions of First Order Logic.Menachem Magidor & Jouko Väänänen - 2011 - Journal of Mathematical Logic 11 (1):87-113.
  13.  23
    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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  14.  23
    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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  15.  17
    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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  16.  2
    The Eightfold Way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.
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  17. 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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  18.  13
    The Non-Compactness of Square.James Cummings, Matthew Foreman & Menachem Magidor - 2003 - Journal of Symbolic Logic 68 (2):637-643.
  19.  1
    Omitting Types in Logic of Metric Structures.Ilijas Farah & Menachem Magidor - forthcoming - Journal of Mathematical Logic.
    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 theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a model of a theory T in a countable language. (...)
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  20.  1
    On the Spectrum of Characters of Ultrafilters.Shimon Garti, Menachem Magidor & Saharon Shelah - forthcoming - Notre Dame Journal of Formal Logic.
    We show that the character spectrum Spχ may include any prescribed set of regular cardinals between λ and 2λ.
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  21.  14
    Chang's Conjecture and Powers of Singular Cardinals.Menachem Magidor - 1977 - Journal of Symbolic Logic 42 (2):272-276.
  22.  10
    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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  23.  9
    Some Highly Undecidable Lattices.Menachem Magidor, John W. Rosenthal, Mattiyahu Rubin & Gabriel Srour - 1990 - Annals of Pure and Applied Logic 46 (1):41-63.
  24.  9
    The Monadic Theory of Ω 2.Yuri Gurevich, Menachem Magidor & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (2):387-398.
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  25.  18
    The Monadic Theory of Ω12.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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  26.  5
    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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  27. Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1:35-98.
  28.  11
    On ${\Omega _1}$-Strongly Compact Cardinals.Joan Bagaria & Menachem Magidor - 2014 - Journal of Symbolic Logic 79 (1):266-278.
  29.  7
    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 $\omega_n$ has the tree property for all $2 \leq n < \omega$ and $2^{<\aleph_{\omega}} = \aleph_{\omega}$, then for all $X \in H_{\aleph_{\omega}}$ and $n < \omega, M^#_n$ exists.
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  30.  13
    Countably Decomposable Admissible Sets.Menachem Magidor, Saharon Shelah & Jonathan Stavi - 1984 - Annals of Pure and Applied Logic 26 (3):287-361.
    The known results about Σ 1 -completeness, Σ 1 -compactness, ordinal omitting etc. are given a unified treatment, which yields many new examples. It is shown that the unifying theorem is best possible in several ways, assuming V = L.
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  31.  19
    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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  32.  10
    $0^Sharp$ and Some Forcing Principles. [REVIEW]Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39-46.
  33.  9
    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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  34.  6
    A Model in Which GCH Holds at Successors but Fails at LimitsStrong Ultrapowers and Long Core ModelsCoherent Sequences Versus Radin SequencesSquares, Scales and Stationary Reflection.Arthur W. Apter, James Cummings, Matthew Foreman & Menachem Magidor - 2002 - Bulletin of Symbolic Logic 8 (4):550.
  35.  6
    Silver Jack H.. 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.
  36.  22
    0♯ and Some Forcing Principles.Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39 - 46.
  37.  9
    The Monadic Theory of $Omega^1_2$.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 $\omega_2$ are recursive each in the other" is consistent; and (ii) ZFC + "The full second-order theory of $\omega_2$ is interpretable in the monadic theory of $\omega_2$" is consistent.
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  38.  9
    The Independence of $Delta^1_n$.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350-362.
    In this paper we prove the independence of $\delta^1_n$ for n $\geq$ 3. We show that $\delta^1_4$ can be forced to be above any ordinal of L using set forcing. For $\delta^1_3$ we prove that it can be forced, using set forcing, to be above any L cardinal $\kappa$ such that $\kappa$ is $\Pi_1$ definable without parameters in L. We then show that $\delta^1_3$ cannot be forced by a set forcing to be above every cardinal of L. Finally we present (...)
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  39.  5
    The Weak $Square^Ast$ is Really Weaker Than the Full $Square$.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029-1033.
  40.  7
    Review: Jack H. Silver, Measurable Cardinals and $Deltafrac{1}{3}$ Well-Orderings. [REVIEW]Menachem Magidor - 1974 - Journal of Symbolic Logic 39 (2):330-331.
  41. Review: M. Gitik, All Uncountable Cardinals Can Be Singular. [REVIEW]Menachem Magidor - 1984 - Journal of Symbolic Logic 49 (2):662-663.
  42.  1
    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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  43. Extender Based Forcings.Moti Gitik, Menachem Magidor & William J. Mitchell - 2003 - Bulletin of Symbolic Logic 9 (2):237-241.
     
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  44. The Independence Of.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350-362.
  45. Gitik M.. All Uncountable Cardinals Can Be Singular. Israel Journal of Mathematics, Vol. 35 , Pp. 61–88.Menachem Magidor - 1984 - Journal of Symbolic Logic 49 (2):662-663.
  46. Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay, William N. Reinhardt, Akihiro Kanamori & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1066-1068.
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