46 found
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  1.  34
    Nonmonotonic reasoning, preferential models and cumulative logics.Sarit Kraus, Daniel Lehmann & Menachem Magidor - 1990 - Artificial Intelligence 44 (1-2):167-207.
  2.  23
    (1 other version)What does a conditional knowledge base entail?Daniel Lehmann & Menachem Magidor - 1992 - Artificial Intelligence 55 (1):1-60.
  3.  98
    (2 other versions)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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  4.  37
    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.  62
    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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  6.  70
    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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  7.  75
    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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  8.  24
    (1 other version)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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  9.  72
    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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  10.  75
    A very weak square principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
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  11.  28
    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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  12.  50
    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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  13.  47
    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.  43
    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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  15.  29
    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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  16.  29
    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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  17.  61
    (1 other version)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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  18. The weak □* is really weaker than the full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
  19.  34
    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. 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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  21.  46
    On ${\omega _1}$-strongly compact cardinals.Joan Bagaria & Menachem Magidor - 2014 - Journal of Symbolic Logic 79 (1):266-278.
  22.  21
    Destructibility of the tree property at ${\aleph _{\omega + 1}}$.Yair Hayut & Menachem Magidor - 2019 - Journal of Symbolic Logic 84 (2):621-631.
  23.  24
    Destructibility of the tree property at אω+1.Yair Hayut & Menachem Magidor - forthcoming - Journal of Symbolic Logic:1-10.
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  24.  30
    Chang's conjecture and powers of singular cardinals.Menachem Magidor - 1977 - Journal of Symbolic Logic 42 (2):272-276.
  25.  46
    The non-compactness of square.James Cummings, Matthew Foreman & Menachem Magidor - 2003 - Journal of Symbolic Logic 68 (2):637-643.
  26.  52
    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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  27.  36
    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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  28.  12
    (1 other version)The Monadic Theory of ω 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: For every $S \subseteq \omega, \mathrm{ZFC} +$ "S and the monadic theory of ω 2 are recursive each in the other" is consistent; and ZFC + "The full second-order theory of ω 2 is interpretable in the monadic theory of ω 2 " is consistent.
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  29.  27
    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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  30.  22
    Games with filters I.Matthew Foreman, Menachem Magidor & Martin Zeman - forthcoming - Journal of Mathematical Logic.
    This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call Welch games. Player II having a winning strategy in the Welch game of length [Formula: see text] on [Formula: see text] is equivalent to weak compactness. Winning the game of length [Formula: see text] is equivalent to [Formula: see text] being measurable. We show that for games of intermediate length [Formula: see text], II winning implies (...)
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  31.  42
    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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  32.  26
    Some highly undecidable lattices.Menachem Magidor, John W. Rosenthal, Mattiyahu Rubin & Gabriel Srour - 1990 - Annals of Pure and Applied Logic 46 (1):41-63.
  33. 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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  34.  28
    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.
  35.  17
    The tree property at the two immediate successors of a singular cardinal.James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova & Spencer Unger - 2021 - Journal of Symbolic Logic 86 (2):600-608.
    We present an alternative proof that from large cardinals, we can force the tree property at $\kappa ^+$ and $\kappa ^{++}$ simultaneously for a singular strong limit cardinal $\kappa $. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for $\kappa =\aleph _{\omega ^2}$.
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  36.  20
    Corson reflections.Ilijas Farah & Menachem Magidor - 2021 - Annals of Pure and Applied Logic 172 (5):102908.
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  37.  44
    0♯ and some forcing principles.Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39 - 46.
  38.  24
    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(λ) (for a singular cardinal λ of countable cofinality) may include any prescribed set of regular cardinals between λ and 2λ.
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  39.  29
    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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  40.  16
    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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  41.  43
    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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  42.  31
    (1 other version)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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  43.  28
    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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  44.  21
    (1 other version)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.
  45.  31
    (1 other version)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.
  46.  30
    $0^sharp$ and Some Forcing Principles. [REVIEW]Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39-46.