"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

Compiled by

Eddie Yeghiayan

"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.

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