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  1. Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory.Gregory H. Moore - 1980 - History and Philosophy of Logic 1 (1-2):95-137.
    What has been the historical relationship between set theory and logic? On the one hand, Zermelo and other mathematicians developed set theory as a Hilbert-style axiomatic system. On the other hand, set theory influenced logic by suggesting to Schröder, Löwenheim and others the use of infinitely long expressions. The questions of which logic was appropriate for set theory - first-order logic, second-order logic, or an infinitary logic - culminated in a vigorous exchange between Zermelo and Gödel around 1930.
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  2.  25
    Zermelo's Axiom of Choice. Its Origins, Development, and Influence.Gregory H. Moore - 1984 - Journal of Symbolic Logic 49 (2):659-660.
  3.  85
    Hilbert and the Emergence of Modern Mathematical Logic.Gregory H. Moore - 1997 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1):65-90.
    Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness of propositional logic -results traditionally credited to Bernays and Post. These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its soundness and completeness: a (...)
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  4.  13
    Cantorian Set Theory and Limitation of Size.Gregory H. Moore - 1987 - Journal of Symbolic Logic 52 (2):568-570.
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  5.  64
    The Origins of Zermelo's Axiomatization of Set Theory.Gregory H. Moore - 1978 - Journal of Philosophical Logic 7 (1):307 - 329.
    What gave rise to Ernst Zermelo's axiomatization of set theory in 1908? According to the usual interpretation, Zermelo was motivated by the set-theoretic paradoxes. This paper argues that Zermelo was primarily motivated, not by the paradoxes, but by the controversy surrounding his 1904 proof that every set can be wellordered, and especially by a desire to preserve his Axiom of Choice from its numerous critics. Here Zermelo's concern for the foundations of mathematics diverged from Bertrand Russell's on the one hand (...)
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  6.  62
    Early History of the Generalized Continuum Hypothesis: 1878—1938.Gregory H. Moore - 2011 - Bulletin of Symbolic Logic 17 (4):489-532.
    This paper explores how the Generalized Continuum Hypothesis (GCH) arose from Cantor's Continuum Hypothesis in the work of Peirce, Jourdain, Hausdorff, Tarski, and how GCH was used up to Gödel's relative consistency result.
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  7.  41
    The Dual Cantor-Bernstein Theorem and the Partition Principle.Bernhard Banaschewski & Gregory H. Moore - 1990 - Notre Dame Journal of Formal Logic 31 (3):375-381.
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  8.  25
    The Roots of Russell's Paradox.Gregory H. Moore - 1988 - Russell: The Journal of Bertrand Russell Studies 8 (1):46.
  9.  89
    Collected Works of Kurt Godel 1938-1974.Georg Kreisel, Kurt Godel, Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay & Jean van Heijenoort - 1991 - Journal of Symbolic Logic 56 (3):1085.
  10. Kurt Gödel: Collected Works, Vol. I: Publications 1929-1936.Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore & Robert M. Solovay - 1998 - Mind 107 (425):219-232.
  11.  54
    Historians and Philosophers of Logic: Are They Compatible? The Bolzano-Weierstrass Theorem as a Case Study.Gregory H. Moore - 1999 - History and Philosophy of Logic 20 (3-4):169-180.
    This paper combines personal reminiscences of the philosopher John Corcoran with a discussion of certain conflicts between historians of logic and philosophers of logic. Some mistaken claims about the history of the Bolzano-Weierstrass Theorem are analyzed in detail and corrected.
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  12. Collected Works, Volume I, Publications 1929-1936.Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore & Robert M. Solovay - 1987 - Mind 96 (384):570-575.
     
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  13. The Collected Papers of Bertrand Russell, Volume 3: Toward the 'Principles of Mathematics' 1900-02.Gregory H. Moore (ed.) - 1994 - Routledge.
    This volume shows Russell in transition from a neo-Kantian and neo-Hegelian philosopher to an analytic philosopher of the first rank. During this period his research centred on writing The Principles of Mathematics where he drew together previously unpublished drafts. These shed light on Russell's paradox. This material will alter previous accounts of how he discovered his paradox and the related paradox of the largest cardinal. The volume also includes a previously unpublished draft of an early attempt to solve his paradox, (...)
     
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  14.  2
    The Collected Papers of Bertrand Russell, Volume 5: Toward Principia Mathematica, 1905–08.Gregory H. Moore (ed.) - 2014 - Routledge.
    This volume of Bertrand Russell's _Collected Papers_ finds Russell focused on writing _Principia Mathematica_ during 1905–08. Eight previously unpublished papers shed light on his different versions of a substitutional theory of logic, with its elimination of classes and relations, during 1905-06. A recurring issue for him was whether a type hierarchy had to be part of a substitutional theory. In mid-1907 he began writing up the final version of _Principia_, now using a ramified theory of types, and eleven unpublished drafts (...)
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  15.  15
    Michael Hallett. Cantorian Set Theory and Limitation of Size. Oxford Logic Guidelines, No. 10. Clarendon Press, Oxford University Press, Oxford and New York1984, Xxiii + 343 Pp. [REVIEW]Gregory H. Moore - 1987 - Journal of Symbolic Logic 52 (2):568-570.
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    The Russell–Peano Connection [Review of Hubert C. Kennedy, Peano: Life and Works of Giuseppe Peano].Gregory H. Moore - 1980 - Russell: The Journal of Bertrand Russell Studies 37.
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  17.  16
    Review: Michael Hallett, Cantorian Set Theory and Limitation of Size. [REVIEW]Gregory H. Moore - 1987 - Journal of Symbolic Logic 52 (2):568-570.
  18.  10
    José Ferreirós. Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics. Xxv + 466 Pp., Illus. Second Revised Edition. Basel/Boston: Birkhäuser, 2007. $79.95. [REVIEW]Gregory H. Moore - 2010 - Isis 101 (4):895-896.
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  19. Lebesgue's Measure Problem and Zermelo's Axiom of Choice.Gregory H. Moore - 1983 - In Joseph Warren Dauben & Virginia Staudt Sexton (eds.), History and Philosophy of Science: Selected Papers. New York Academy of Sciences.
  20.  19
    Russell and the Development of Mathematics [Review of George Temple, 100 Years of Mathematics].Gregory H. Moore - 1985 - Russell: The Journal of Bertrand Russell Studies 5 (1):89.