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Akihiro Kanamori
Boston University
  1.  8
    Handbook of Mathematical Logic.Akihiro Kanamori - 1984 - Journal of Symbolic Logic 49 (3):971-975.
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  2.  41
    Cohen and Set Theory.Akihiro Kanamori - 2008 - Bulletin of Symbolic Logic 14 (3):351-378.
    We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.
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  3. The Mathematical Development of Set Theory From Cantor to Cohen.Akihiro Kanamori - 1996 - Bulletin of Symbolic Logic 2 (1):1-71.
    Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...)
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  4.  52
    The Empty Set, the Singleton, and the Ordered Pair.Akihiro Kanamori - 2003 - Bulletin of Symbolic Logic 9 (3):273-298.
  5.  5
    Perfect-Set Forcing for Uncountable Cardinals.Akihiro Kanamori - 1980 - Annals of Mathematical Logic 19 (1-2):97-114.
  6.  62
    Zermelo and Set Theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.
    Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...)
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  7.  37
    Gödel and Set Theory.Akihiro Kanamori - 2007 - Bulletin of Symbolic Logic 13 (2):153-188.
    Kurt Gödel with his work on the constructible universeLestablished the relative consistency of the Axiom of Choice and the Continuum Hypothesis. More broadly, he ensured the ascendancy of first-order logic as the framework and a matter of method for set theory and secured the cumulative hierarchy view of the universe of sets. Gödel thereby transformed set theory and launched it with structured subject matter and specific methods of proof. In later years Gödel worked on a variety of set theoretic constructions (...)
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  8.  11
    Mathematical Knowledge : Motley and Complexity of Proof.Akihiro Kanamori - 2013 - Annals of the Japan Association for Philosophy of Science 21:21-35.
  9.  98
    Hilbert and Set Theory.Burton Dreben & Akihiro Kanamori - 1997 - Synthese 110 (1):77-125.
  10.  95
    The Mathematical Import of Zermelo's Well-Ordering Theorem.Akihiro Kanamori - 1997 - Bulletin of Symbolic Logic 3 (3):281-311.
    Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...)
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  11.  61
    In Praise of Replacement.Akihiro Kanamori - 2012 - Bulletin of Symbolic Logic 18 (1):46-90.
    This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.
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  12.  33
    Bernays and Set Theory.Akihiro Kanamori - 2009 - Bulletin of Symbolic Logic 15 (1):43-69.
    We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles.
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  13.  6
    On Gödel Incompleteness and Finite Combinatorics.Akihiro Kanamori & Kenneth McAloon - 1987 - Annals of Pure and Applied Logic 33 (1):23-41.
  14.  30
    Levy and Set Theory.Akihiro Kanamori - 2006 - Annals of Pure and Applied Logic 140 (1):233-252.
    Azriel Levy did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcing and definability will continue to be basic to the subject. What follows is a detailed account and analysis of Levy’s work and contributions (...)
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  15.  3
    Mathias and Set Theory.Akihiro Kanamori - 2016 - Mathematical Logic Quarterly 62 (3):278-294.
    On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.
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  16.  23
    Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics.Akihiro Kanamori - 2001 - Bulletin of Symbolic Logic 7 (2):277-278.
  17. Handbook of the History of Logic.Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.) - 2004 - Elsevier.
    Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and (...)
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  18.  12
    Set, or Null Class, Provides an Entrée Into Our Main Themes, Particularly The.Akihiro Kanamori - 2003 - Bulletin of Symbolic Logic 9 (3):273-298.
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  19.  10
    Finest Partitions for Ultrafilters.Akihiro Kanamori - 1986 - Journal of Symbolic Logic 51 (2):327-332.
  20.  16
    Alternative Set Theories.Thierry Libert, T. Forster, R. Holmes, Dov M. Gabbay, John Woods & Akihiro Kanamori - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier.
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  21.  7
    Ü1. Beginnings. Zermelo, Born at the Time Cantor Was Making His First Incursions Into the Transfinite, Would Make the First Large Moves in Set Theory. [REVIEW]Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.
    Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...)
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  22.  14
    Regressive Partitions and Borel Diagonalization.Akihiro Kanamori - 1989 - Journal of Symbolic Logic 54 (2):540-552.
  23.  7
    Regressive Partition Relations, N-Subtle Cardinals, and Borel Diagonalization.Akihiro Kanamori - 1991 - Annals of Pure and Applied Logic 52 (1-2):65-77.
    We consider natural strengthenings of H. Friedman's Borel diagonalization propositions and characterize their consistency strengths in terms of the n -subtle cardinals. After providing a systematic survey of regressive partition relations and their use in recent independence results, we characterize n -subtlety in terms of such relations requiring only a finite homogeneous set, and then apply this characterization to extend previous arguments to handle the new Borel diagonalization propositions.
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  24.  30
    Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005.Matthias Aschenbrenner, Alexander Berenstein, Andres Caicedo, Joseph Mileti, Bjorn Poonen, W. Hugh Woodin & Akihiro Kanamori - 2005 - Bulletin of Symbolic Logic 11 (3).
  25.  18
    Montréal, Québec, Canada May 17–21, 2006.Jeremy Avigad, Sy Friedman, Akihiro Kanamori, Elisabeth Bouscaren, Philip Kremer, Claude Laflamme, Antonio Montalbán, Justin Moore & Helmut Schwichtenberg - 2007 - Bulletin of Symbolic Logic 13 (1).
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  26. REVIEWS-Labyrinth of Thought.J. Ferreiros & Akihiro Kanamori - 2001 - Bulletin of Symbolic Logic 7 (2):277-277.
  27. Sets and Extensions in the Twentieth Century.Dov M. Gabbay, Akihiro Kanamori & John Woods - 2004 - In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic. Elsevier.
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  28. REVIEWS-Moti Gitik's Recent Papers on the Singular Cardinals Problem.Moti Gitik & Akihiro Kanamori - 2003 - Bulletin of Symbolic Logic 9 (2):237-241.
  29. Analytic Philosophy & Logic.Akihiro Kanamori - 2000
  30. E-Mail: Aki@ Math. Bu. Edu.Akihiro Kanamori - 2005 - Bulletin of Symbolic Logic 11 (2).
  31.  11
    Erdős and Set Theory.Akihiro Kanamori - 2014 - Bulletin of Symbolic Logic 20 (4):449-490,.
    Paul Erdős was a mathematicianpar excellencewhose results and initiatives have had a large impact and made a strong imprint on the doing of and thinking about mathematics. A mathematician of alacrity, detail, and collaboration, Erdős in his six decades of work moved and thought quickly, entertained increasingly many parameters, and wrote over 1500 articles, the majority with others. Hismodus operandiwas to drive mathematics through cycles of problem, proof, and conjecture, ceaselessly progressing and ever reaching, and hismodus vivendiwas to be itinerant (...)
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  32.  5
    G Ödel has Emphasized the Important Role That His Philosophical Views Had Played in His Discoveries. Thus, in a Letter to Hao Wang of December 7, 1967, Explaining Why Skolem and Others Had Not Obtained the Completeness Theorem for Predicate Calculus, Gödel Wrote: This Blindness (or Prejudice, or Whatever You May Call It) of Logicians. [REVIEW]Akihiro Kanamori - 2005 - Bulletin of Symbolic Logic 11 (2).
  33.  12
    Handbook of Mathematical Logic, Edited by Barwise Jon with the Cooperation of Keisler H. J., Kunen K., Moschovakis Y. N., and Troelstra A. S., Studies in Logic and the Foundations of Mathematics, Vol. 90, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1978 , Xi + 1165 Pp. [REVIEW]Akihiro Kanamori - 1984 - Journal of Symbolic Logic 49 (3):971-975.
  34.  8
    Introduction.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (1):3.
  35.  7
    José Ferreirós. Labyrinth of Thought. A History of Set Theory and its Role in Modern Mathematics. Science Networks, Vol. 23. Birkhäuser Verlag, Basel, Boston, and Berlin, 1999, Xxi + 440 Pp. [REVIEW]Akihiro Kanamori - 2001 - Bulletin of Symbolic Logic 7 (2):277-278.
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  36.  37
    Jack Silver. On the Singular Cardinals Problem. Proceedings of the International Congress of Mathematicians, Vancouver 1974, Vol. 1, Canadian Mathematical Congress, Montreal1975, Pp. 265–268. - Fred Galvin and András Hajnal. Inequalities for Cardinal Powers. Annals of Mathematics, Ser. 2 Vol. 101 , Pp. 491–498. - Keith J. Devlin and R. B. Jensen. Marginalia to a Theorem of Silver. ISILC Logic Conference, Proceedings of the International Summer Institute and Logic Colloquium, Kiel 1974, Edited by G. H. Müller, A. Obsrschelp, and K. Potthoff, Lecture Notes in Mathematics, Vol. 499, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, Pp. 115–142. - Menachem Maoidor. On the Singular Cardinals Problem I. Israel Journal of Mathematics, Vol. 28 , Pp. 1–31. - Menachem Magidor. On the Singular Cardinals Problem II. Annals of Mathematics, Ser. 2 Vol. 106 , Pp. 517–547. [REVIEW]Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
  37.  13
    Laver and Set Theory.Akihiro Kanamori - 2016 - Archive for Mathematical Logic 55 (1-2):133-164.
    In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.
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  38.  13
    Moti Gitik and Menachem Magidor. Extender Based Forcings. The Journal of Symbolic Logic, Vol. 59 , Pp. 445–460. - Moti Gitik and William J. Mitchell. Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis. Annals of Pure and Applied Logic, Vol. 82 , Pp. 273–316. - Moti Gitik. Blowing Up the Power of a Singular Cardinal. Annals of Pure and Applied Logic, Vol. 80 , Pp. 17–33. - Moti Gitik and Carmi Merimovich. Possible Values for And. Annals of Pure and Applied Logic, Vol. 90 , Pp. 193–241. - Moti Gitik. Blowing Up Power of a Singular Cardinal—Wider Gaps. Annals of Pure and Applied Logic, Vol. 116 , Pp. 1–38. [REVIEW]Akihiro Kanamori - 2003 - Bulletin of Symbolic Logic 9 (2):237-241.
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  39. [Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
  40.  2
    Preface.Akihiro Kanamori - 2005 - Bulletin of Symbolic Logic 11 (2):131.
  41. Putnam’s Constructivization Argument.Akihiro Kanamori - 2018 - In Roy Cook & Geoffrey Hellman (eds.), Hilary Putnam on Logic and Mathematics. Springer Verlag.
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  42.  17
    Review: Jon Barwise, H. J. Keisler, K. Kunen, Y. N. Moschovakis, A. S. Troelstra, Handbook of Mathematical Logic; J. R. Shoenfield, B.1. Axioms of Set Theory. [REVIEW]Akihiro Kanamori - 1984 - Journal of Symbolic Logic 49 (3):971-975.
  43.  12
    Review: Saharon Shelah, Cardinal Arithmetic. [REVIEW]Akihiro Kanamori - 1997 - Journal of Symbolic Logic 62 (3):1035-1039.
  44.  22
    Shelah Saharon. Cardinal Arithmetic. Oxford Logic Guides, No. 29. Clarendon Press, Oxford University Press, Oxford and New York1994, Xxxi + 481 Pp. [REVIEW]Akihiro Kanamori - 1997 - Journal of Symbolic Logic 62 (3):1035-1039.
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  45. Set Theory. Gödel and Set Theory.Akihiro Kanamori - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
     
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  46.  23
    The Compleat 0†.Akihiro Kanamori & Tamara Awerbuch-Friedlander - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (2):133-141.
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  47. The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
     
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  48. The Higher Infinite Large Cardinals in Set Theory From Their Beginnings.Akihiro Kanamori - 1994
  49. The Infinite as Method in Set Theory and Mathematics.Akihiro Kanamori - 2009 - Ontology Studies: Cuadernos de Ontología:31-41.
    Este artículo da cuenta de la aparición histórica de lo infinito en la teoría de conjuntos, y de cómo lo tratamos dentro y fuera de las matemáticas. La primera sección analiza el surgimiento de lo infinito como una cuestión de método en la teoría de conjuntos. La segunda sección analiza el infinito dentro y fuera de las matemáticas, y cómo deben adoptarse. This article address the historical emergence of the infinite in set theory, and how we are to take the (...)
     
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  50.  10
    The Journal of Symbolic Logic.Akihiro Kanamori - 2003 - Bulletin of Symbolic Logic 9 (2):237-241.
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