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24Alternative Set TheoriesIn Dov Gabbay (ed.), The Handbook of the History of Logic, Elsevier. 2009.
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Sets and extensions in the twentieth centuryIn Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the history of logic, Elsevier. 2004.
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164Handbook of the history of logic (edited book)Elsevier. 2004.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, includ…Read more
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232000 Annual Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 6 (3): 361-396. 2000.
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The Proceedings of the Twentieth World Congress of PhilosophyThe Proceedings of the Twentieth World Congress of Philosophy 6. 2000.Analytic philosophy, a dominant tradition of twentieth-century philosophy, can be informatively cast as the outgrowth of the investigations of logic and language of Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein, and in the next generation, of Rudolf Carnap and W.V. Quine. As such, it is a specific historical development, one that featured subtle dialectical interactions among its propounders, interactions that have been reflected or reenacted in later developments. Whatever its herita…Read more
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17Shelah Saharon. Cardinal arithmetic. Oxford logic guides, no. 29. Clarendon Press, Oxford University Press, Oxford and New York1994, xxxi + 481 pp (review)Journal of Symbolic Logic 62 (3): 1035-1039. 1997.
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12José 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)Bulletin of Symbolic Logic 7 (2): 277-278. 2001.
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Putnam’s Constructivization ArgumentIn John Burgess (ed.), Hilary Putnam on Logic and Mathematics, Springer Verlag. 2018.
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22Mathias and set theoryMathematical Logic Quarterly 62 (3): 278-294. 2016.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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29Mathematical Knowledge : Motley and Complexity of ProofAnnals of the Japan Association for Philosophy of Science 21 21-35. 2013.
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24The Mathematical Infinite as a Matter of MethodAnnals of the Japan Association for Philosophy of Science 20 3-15. 2012.
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23Review: 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)Journal of Symbolic Logic 49 (3): 971-975. 1984.
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25On Gödel incompleteness and finite combinatoricsAnnals of Pure and Applied Logic 33 (C): 23-41. 1987.
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108Zermelo and set theoryBulletin of Symbolic Logic 10 (4): 487-553. 2004.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 framewo…Read more
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14G 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)Bulletin of Symbolic Logic 11 (2). 2005.
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54Bernays and set theoryBulletin of Symbolic Logic 15 (1): 43-69. 2009.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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17Set, or Null class, provides an entrée into our main themes, particularly theBulletin of Symbolic Logic 9 (3): 273-298. 2003.
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49Levy and set theoryAnnals of Pure and Applied Logic 140 (1): 233-252. 2006.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…Read more
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29Erdős and set theoryBulletin of Symbolic Logic 20 (4). 2014.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 progressin…Read more
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11REVIEWS-Moti Gitik's recent papers on the Singular Cardinals ProblemBulletin of Symbolic Logic 9 (2): 237-241. 2003.
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Boston UniversityRegular Faculty
Boston, Massachusetts, United States of America
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |