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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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Structures and the Hyperarithmetical Hierarchy. Knight has directed or co-directed seven doctoral dissertations in mathematics and one in electrical engineering. She served on selection panels for the NSF Postdoctoral Fellowships, on program committees of numerous meetings, and as an editor of The Journal of Symbolic Logic (1989-1995) (review)Bulletin of Symbolic Logic 6 (1). 2000.
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17Regressive partition relations, n-subtle cardinals, and Borel diagonalizationAnnals of Pure and Applied Logic 52 (1-2): 65-77. 1991.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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123The mathematical import of zermelo's well-ordering theoremBulletin of Symbolic Logic 3 (3): 281-311. 1997.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…Read more
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102Cohen and set theoryBulletin of Symbolic Logic 14 (3): 351-378. 2008.We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing
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28The compleat 0†Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (2): 133-141. 1990.
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Proceedings of the 20th World Conress of Philosophy, Vol VI , Analytic Philosophy and Logic (edited book)Philosophy Document Center. 2000.
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29Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics (review)Bulletin of Symbolic Logic 7 (2): 277-278. 2001.
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69Gödel and set theoryBulletin of Symbolic Logic 13 (2): 153-188. 2007.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…Read more
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52004–05 Winter Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 11 (3): 454-460. 2005.
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The Infinite as Method in Set Theory and MathematicsOntology Studies: Cuadernos de Ontología 31-41. 2009.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 infinite in and out of mathematics.Th…Read more
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17Review: Saharon Shelah, Cardinal Arithmetic (review)Journal of Symbolic Logic 62 (3): 1035-1039. 1997.
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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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91The 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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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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24On Gödel incompleteness and finite combinatoricsAnnals of Pure and Applied Logic 33 (C): 23-41. 1987.
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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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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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Boston UniversityRegular Faculty
Boston, Massachusetts, United States of America
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |