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81In praise of replacementBulletin of Symbolic Logic 18 (1): 46-90. 2012.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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88The empty set, the Singleton, and the ordered pairBulletin of Symbolic Logic 9 (3): 273-298. 2003.For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Ch…Read more
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22Review: 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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24On Gödel incompleteness and finite combinatoricsAnnals of Pure and Applied Logic 33 (C): 23-41. 1987.
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106Zermelo 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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53Bernays 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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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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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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49Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005Bulletin of Symbolic Logic 11 (3). 2005.
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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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362004–05 Winter Meeting of the Association for Symbolic Logic (review)Bulletin of Symbolic Logic 11 (3): 454-460. 2005.
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Boston UniversityRegular Faculty
Boston, Massachusetts, United States of America
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |