"The Empty Set, the Singleton, and the Ordered Pair"
Abstract: "For the modern set theorist the empty set 0 , the
singleton {a} , and the ordered pair
Akihiro Kanamori
Department of Mathematics
Boston University
Tuesday, March 5, 2002
4:30 pm
SST 777
"Characterization of Nonregular Ultrafilters." Notices. American Mathematical Society (1974), 21(3):A381.
"P-Points in Betan." Notices. American Mathematical Society (1975), 22(7):A717.
"Ultrafilters over a Measurable Cardinal." Annals of Mathematical Logic (1976), 10:315-356.
"Weakly Normal Filters and Irregular Ultrafilters." Transactions of the American Mathematical Society (June 1976), 220:393-399.
(with Robert M. Solovay and William N. Reinhardt.) "Strong Axioms of Infinity and Elementary Embeddings." Annals of Mathematical Logic (1978), 13(1):73-116.
"Perfect Set Forcing for Uncountable Cardinals." Annals of Mathematical Logic (1980), 19(1-2):97-114.
"On P-Points over a Measurable Cardinal." Journal of Symbolic Logic (1981), 46(1):59-66.
"On Silver's and Related Principles."
In D. Van Dalen, D. Lascar, T.J. Smiley, eds., Logic Colloquium '80, pp. 153-172. Studies in Logic and the Foundations of Mathematics, 108. Amsterdam & New York: North-Holland, 1982.
Logic Colloquium, 1980, Prague, Czechoslovakia.
"Morasses in Combinatorial Set Theory." In A.R.D. Mathias, ed., Surveys in Set Theory, pp. 167-196. London Mathematical Society Lecture Note Series, 87. Cambridge & New York: Cambridge University Press, 1983.
(with James M. Henle and E.M. Kleinberg.) "Filters for Square Bracket Partition Relations." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (1984), 30(2):183-192.
"Negative Partition Relations for Ultrafilters for Uncountable Cardinals." Proceedings of the American Mathematical Society (1984), 92(1):83-89.
Review of the set theory articles in Jon Barwise, et al., Handbook of Mathematical Logic. Journal of Symbolic Logic (September 1984), 49(3):971-975.
(with A.D. Taylor.) "Separating Ultrafilters on Uncountable Cardinals." Israel Journal of Mathematics (1984), 47(2-3):131-138.
"Finest Partitions for Ultrafiletrs." Journal of Symbolic Logic (June 1986), 51(2):327-332.
"A Mathematical Incompleteness in Peano Arithmetic Involving a Theorem of Erdos and Rado." Journal of Symbolic Logic (December 1986), 51(4):1098.
"Partition Relations for Successor Cardinals." Advances in Mathematics (February 1986), 59(2):152-169.
(with Kenneth McAllon.) "On Gödel Incompleteness and Finite Combinatorics." Annals of Pure and Applied Logic (January 1987), 33(1):23-41.
(with András Hajnal and Saharon Shelah.) "Regressive Partition Relations for Infinite Cardinals." Transactions of the American Mathematical Society (January 1987), 299(1):145-154.
"Diamonds, Large Cardinals, and Ultrafilters." In Walter A. Carnielli and Luiz Paulo de Alcantara, eds., Matheods and Applications of Mathematical Logic: Proceedings of the VII
Latin American Symposium on Mathematical Logic held July 29-August 2, 1985, pp. 35-42. Contemporary Mathematics (American Mathematical Society, Vol. 69. Providence, RI: American Mathematical Society, 1988.
Latin-American Symposium on Mathematical Logic, 7th, 1985: State University of Campinas.
"Regressive Partitions and Borel Diagonalization." Journal of Symbolic Logic (June 1989), 54(2):540-552.
(with Tamara Awerbuch-Friedlander.) "The Compleat Zero-Dagger." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (1990), 36(2):133-141.
"Regressive Partition Relations, N-Subtle Cardinals, and Borel
Diagonalization."
Annals of Pure and Applied Logic, (April 15, 1991), 52(1-2):65-77.
International Symposium on Mathematical Logic and its Applications, Nagoya, 1988.
The Higher Infinite: Large Cardinals in Set Theory from their Beginnings. Perspectives in Mathematical Logic. Berlin & New York: Springer-Verlag, 1994.
(with Saharon Shelah.) "Complete Quotient Boolean Algebras." Transactions of the American Mathematical Society (June 1995), 347(6):1963-1979.
"The Emergence of Descriptive Set Theory." Synthese (1995), 251:241-262. Reprinted in Jaakko Hintikka, ed., From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics, pp. 241-262. Synthese Library, 251. Dordrecht: Kluwer, 1995.
"The Mathematical Development of Set Theory from Cantor to Cohen." Bulletin of Symbolic Logic (1996), 2(1):1-71.
(with Burton Dreben.) "Hilbert and Set theory."
Synthese (January 1997), 110(1):77-125.
This issue is entitled "Symposium
David Hilbert," and is edited by Akihiro Kanamori and A. Tauber.
"The Mathematical Import of Zermelo's Well-Ordering Theorem." Bulletin of Symbolic Logic (1997), 3(3):281-311.
"Preface." Synthese (May 1997), 111(2):131-132.
Review of Saharon Shelah's "Cardinal Arithmetic." Journal of Symbolic Logic (September 1997), 62(3):1035-1039.
Edited. The Proceedings of the Twentieth World Congress of Philosophy, Volume 6: Analytic Philosophy & Logic. Bowling Green, OH: Philosophy Documentation Center, Bowling Green State University, 2000.