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Matthew Foreman [32]Matthew D. Foreman [2]
  1.  33
    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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  2.  2
    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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  3.  24
    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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  4.  24
    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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  5.  19
    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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  6.  13
    Diagonal Prikry Extensions.James Cummings & Matthew Foreman - 2010 - Journal of Symbolic Logic 75 (4):1383-1402.
  7.  30
    A Very Weak Square Principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
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  8.  19
    Games Played on Boolean Algebras.Matthew Foreman - 1983 - Journal of Symbolic Logic 48 (3):714-723.
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  9.  10
    The Club Guessing Ideal: Commentary on a Theorem of Gitik and Shelah.Matthew Foreman & Peter Komjath - 2005 - Journal of Mathematical Logic 5 (1):99-147.
    It is shown in this paper that it is consistent for various club guessing ideals to be saturated.
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  10.  32
    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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  11.  12
    Chang’s Conjecture, Generic Elementary Embeddings and Inner Models for Huge Cardinals.Matthew Foreman - 2015 - Bulletin of Symbolic Logic 21 (3):251-269.
    We introduce a natural principleStrong Chang Reflectionstrengthening the classical Chang Conjectures. This principle is between a huge and a two huge cardinal in consistency strength. In this note we prove that it implies the existence of an inner model with a huge cardinal. The technique we explore for building inner models with huge cardinals adapts to show thatdecisiveideals imply the existence of inner models with supercompact cardinals. Proofs for all of these claims can be found in [10].1,2.
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  12.  16
    Donald A. Martin and John R. Steel. Projective Determinacy. Proceedings of the National Academy of Sciences of the United States of America, Vol. 85 , Pp. 6582–6586. - W. Hugh Woodin. Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees. Proceedings of the National Academy of Sciences of the United States of America, Vol. 85 , Pp. 6587–6591. - Donald A. Martin and John R. Steel. A Proof of Projective Determinacy. Journal of the American Mathematical Society, Vol. 2 , Pp. 71–125. [REVIEW]Matthew D. Foreman - 1992 - Journal of Symbolic Logic 57 (3):1132-1136.
  13.  18
    The Non-Compactness of Square.James Cummings, Matthew Foreman & Menachem Magidor - 2003 - Journal of Symbolic Logic 68 (2):637-643.
  14.  13
    Some Problems in Singular Cardinals Combinatorics.Matthew Foreman - 2005 - Notre Dame Journal of Formal Logic 46 (3):309-322.
    This paper attempts to present and organize several problems in the theory of Singular Cardinals. The most famous problems in the area (bounds for the ℶ-function at singular cardinals) are well known to all mathematicians with even a rudimentary interest in set theory. However, it is less well known that the combinatorics of singular cardinals is a thriving area with results and problems that do not depend on a solution of the Singular Cardinals Hypothesis. We present here an annotated collection (...)
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  15.  13
    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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  16.  39
    Review: Stan Wagon, The Branch-Tarski Paradox; Stan Wagon, The Branch-Tarski Paradox. [REVIEW]Matthew Foreman - 1995 - Journal of Symbolic Logic 60 (2):698-698.
  17.  3
    The Complexity of Antidifferentiation.Randall Dougherty, Alexander S. Kechris, Ferenc Beleznay & Matthew Foreman - 2001 - Bulletin of Symbolic Logic 7 (3):385-388.
  18.  24
    Forbidden Intervals.Matthew Foreman - 2009 - Journal of Symbolic Logic 74 (4):1081 - 1099.
  19.  21
    $0^Sharp$ and Some Forcing Principles. [REVIEW]Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39-46.
  20.  22
    Wagon Stan. The Banach–Tarski Paradox. Encyclopedia of Mathematics and its Applications, Vol. 24. Cambridge University Press, Cambridge, New York, and Melbourne, 1985, Xvi+ 251 Pp. Wagon Stan. The Banach–Tarski Paradox. Paperbound Edition of the Preceding. Cambridge University Press, Cambridge, New York, and Melbourne, 1993, Xviii+ 253 Pp. [REVIEW]Matthew Foreman - 1995 - Journal of Symbolic Logic 60 (2):698-698.
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  21.  17
    Banach-Tarski Paradox Using Pieces with the Property of Baire.Randall Dougherty & Matthew Foreman - 2001 - Bulletin of Symbolic Logic 7 (4):537-538.
  22.  14
    New Orleans Marriott and Sheraton New Orleans New Orleans, Louisiana January 7–8, 2007.Matthew Foreman, Su Gao, Valentina Harizanov, Ulrich Kohlenbach, Michael Rathjen, Reed Solomon, Carol Wood & Marcia Groszek - 2007 - Bulletin of Symbolic Logic 13 (3).
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  23.  24
    0♯ and Some Forcing Principles.Matthew Foreman, Menachem Magidor & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (1):39 - 46.
  24.  11
    Phoenix Civic Plaza, Phoenix, Arizona, January 9–10, 2004.Matthew Foreman, Steve Jackson, Julia Knight, R. W. Knight, Steffen Lempp, Françoise Point, Kobi Peterzil, Leonard Schulman, Slawomir Solecki & Carol Wood - 2004 - Bulletin of Symbolic Logic 10 (2).
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  25. 2003 European Summer Meeting of the Association for Symbolic Logic Logic Colloquim'03.Michael Benedikt, Stevo Todorcevic, Alexandru Baltag, Howard Becker, Matthew Foreman, Jean-Yves Girard, Martin Grohe, Peter T. Johnstone, Simo Knuuttila & Menachem Kojman - 2004 - Bulletin of Symbolic Logic 10 (2).
  26.  11
    Review: Donald A. Martin, John R. Steel, Projective Determinacy; W. Hugh Woodin, Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees; Donald A. Martin, John R. Steel, A Proof of Projective Determinacy. [REVIEW]Matthew D. Foreman - 1992 - Journal of Symbolic Logic 57 (3):1132-1136.
  27.  6
    A Descriptive View of Ergodic Theory.Matthew Foreman, M. Foreman, A. S. Kechris, A. Louveau, B. Weiss & Alexander S. Kechris - 2001 - Bulletin of Symbolic Logic 7 (4):545-546.
  28.  6
    Review: T. Jech, Multiple Forcing. [REVIEW]Matthew Foreman - 1989 - Journal of Symbolic Logic 54 (3):1112-1113.
  29.  4
    Generic Graph Construction.James E. Baumgartner, Matthew Foreman, Richard Laver, Saharon Shelah & A. Baker - 2001 - Bulletin of Symbolic Logic 7 (4):539-541.
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  30.  6
    Introduction to the Special Issue on Singular Cardinals Combinatorics.Matthew Foreman - 2005 - Notre Dame Journal of Formal Logic 46 (3):249.