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  1. Brent Cody & Menachem Magidor (2014). On Supercompactness and the Continuum Function. 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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  2. Menachem Magidor & Jouko Väänänen (2011). On Löwenheim–Skolem–Tarski Numbers for Extensions of First Order Logic. Journal of Mathematical Logic 11 (01):87-113.
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  3. Sy-David Friedman & Menachem Magidor (2009). The Number of Normal Measures. 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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  4. James Cummings, Matthew Foreman & Menachem Magidor (2006). Canonical Structure in the Universe of Set Theory: Part Two. 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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  5. James Cummings, Matthew Foreman & Menachem Magidor (2004). Canonical Structure in the Universe of Set Theory: Part One. 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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  6. James Cummings, Matthew Foreman & Menachem Magidor (2003). The Non-Compactness of Square. Journal of Symbolic Logic 68 (2):637-643.
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  7. James Cummings, Matthew Foreman & Menachem Magidor (2001). Squares, Scales and Stationary Reflection. Journal of Mathematical Logic 1 (01):35-98.
  8. James Cummings, Matthew Foreman & Menachem Magidor (2001). Scales, Squares and Reflection. Journal of Mathematical Logic 1:35-98.
     
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  9. Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler (2001). The Consistency Strength of Successive Cardinals with the Tree Property. 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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  10. Daniel Lehmann, Menachem Magidor & Karl Schlechta (2001). Distance Semantics for Belief Revision. 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. Amir Leshem & Menachem Magidor (1999). The Independence of Δ1n. 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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  12. Amir Leshem & Menachem Magidor (1999). The Independence of $Delta^1_n$. 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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  13. Matthew Foreman & Menachem Magidor (1997). A Very Weak Square Principle. Journal of Symbolic Logic 62 (1):175-196.
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  14. Menachem Magidor & Saharon Shelah (1996). The Tree Property at Successors of Singular Cardinals. 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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  15. Arthur W. Apter & Menachem Magidor (1995). Instances of Dependent Choice and the Measurability Of. 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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  16. Matthew Foreman & Menachem Magidor (1995). Large Cardinals and Definable Counterexamples to the Continuum Hypothesis. 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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  17. Moti Gitik & Menachem Magidor (1994). Extender Based Forcings. 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. Maxim R. Burke & Menachem Magidor (1990). Shelah's Pcf Theory and its Applications. 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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  19. Menachem Magidor, John W. Rosenthal, Mattiyahu Rubin & Gabriel Srour (1990). Some Highly Undecidable Lattices. Annals of Pure and Applied Logic 46 (1):41-63.
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  20. Shai Ben-David & Menachem Magidor (1986). The Weak □* is Really Weaker Than the Full □. Journal of Symbolic Logic 51 (4):1029 - 1033.
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  21. Shai Ben-David & Menachem Magidor (1986). The Weak $Square^Ast$ is Really Weaker Than the Full $Square$. Journal of Symbolic Logic 51 (4):1029-1033.
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  22. Matthew Foreman, Menachem Magidor & Saharon Shelah (1986). 0♯ and Some Forcing Principles. Journal of Symbolic Logic 51 (1):39 - 46.
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  23. Matthew Foreman, Menachem Magidor & Saharon Shelah (1986). $0^Sharp$ and Some Forcing Principles. [REVIEW] Journal of Symbolic Logic 51 (1):39-46.
  24. Menachem Magidor (1984). Review: M. Gitik, All Uncountable Cardinals Can Be Singular. [REVIEW] Journal of Symbolic Logic 49 (2):662-663.
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  25. Menachem Magidor, Saharon Shelah & Jonathan Stavi (1984). Countably Decomposable Admissible Sets. 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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  26. Yuri Gurevich, Menachem Magidor & Saharon Shelah (1983). The Monadic Theory of Ω12. 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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  27. Yuri Gurevich, Menachem Magidor & Saharon Shelah (1983). The Monadic Theory of $Omega^1_2$. 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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  28. Menachem Magidor, Saharon Shelah & Jonathan Stavi (1983). On the Standard Part of Nonstandard Models of Set Theory. 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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  29. Menachem Magidor (1982). Reflecting Stationary Sets. 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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  30. Menachem Magidor (1977). Chang's Conjecture and Powers of Singular Cardinals. Journal of Symbolic Logic 42 (2):272-276.
  31. Menachem Magidor (1976). How Large is the First Strongly Compact Cardinal? Or a Study on Identity Crises. Annals of Mathematical Logic 10 (1):33-57.
  32. Menachem Magidor (1974). Review: Jack H. Silver, Measurable Cardinals and $Deltafrac{1}{3}$ Well-Orderings. [REVIEW] Journal of Symbolic Logic 39 (2):330-331.