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159Handbook 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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222000 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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24Shelah 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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11José 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 Roy Cook & Geoffrey Hellman (eds.), Hilary Putnam on Logic and Mathematics, Springer Verlag. 2018.
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18Mathias 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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27Mathematical Knowledge : Motley and Complexity of ProofAnnals of the Japan Association for Philosophy of Science 21 21-35. 2013.
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23The Mathematical Infinite as a Matter of MethodAnnals of the Japan Association for Philosophy of Science 20 3-15. 2012.
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46Levy 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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27Erdős 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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8REVIEWS-Moti Gitik's recent papers on the Singular Cardinals ProblemBulletin of Symbolic Logic 9 (2): 237-241. 2003.
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19Handbook 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)Journal of Symbolic Logic 49 (3): 971-975. 1984.
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170The mathematical development of set theory from Cantor to CohenBulletin of Symbolic Logic 2 (1): 1-71. 1996.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 crise…Read more
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19Zermelo and Set Theory (review)Bulletin of Symbolic Logic 10 (4): 487-553. 2004.Ernst Friedrich Ferdinand Zermelo (1871–1953) 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 concep…Read more
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49Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005Bulletin of Symbolic Logic 11 (3). 2005.
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1Set theory. Gödel and set theoryIn Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial, Association For Symbolic Logic. 2010.
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11Perfect-set forcing for uncountable cardinalsAnnals of Mathematical Logic 19 (1-2): 97-114. 1980.
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20Laver and set theoryArchive for Mathematical Logic 55 (1-2): 133-164. 2016.In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.
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Boston UniversityRegular Faculty
Boston, Massachusetts, United States of America
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |