-
10REVIEWS-Moti Gitik's recent papers on the Singular Cardinals ProblemBulletin of Symbolic Logic 9 (2): 237-241. 2003.
-
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.
-
22Zermelo 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
-
172The 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
-
50Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005Bulletin of Symbolic Logic 11 (3). 2005.
-
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.
-
13Perfect-set forcing for uncountable cardinalsAnnals of Mathematical Logic 19 (1-2): 97-114. 1980.
-
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.
-
362004–05 Winter Meeting of the Association for Symbolic Logic (review)Bulletin of Symbolic Logic 11 (3): 454-460. 2005.
-
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.
-
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
-
103Cohen 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
-
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
-
31The compleat 0†Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (2): 133-141. 1990.
-
Proceedings of the 20th World Conress of Philosophy, Vol VI , Analytic Philosophy and Logic (edited book)Philosophy Document Center. 2000.
-
29Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics (review)Bulletin of Symbolic Logic 7 (2): 277-278. 2001.
-
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
-
52004–05 Winter Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 11 (3): 454-460. 2005.
-
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
-
17Review: Saharon Shelah, Cardinal Arithmetic (review)Journal of Symbolic Logic 62 (3): 1035-1039. 1997.
-
Boston UniversityRegular Faculty
Boston, Massachusetts, United States of America
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |