Ali Enayat
CONTACT INFORMATION:
Department of Mathematics and Statistics
American University
4400
Washington, DC
e-mail : enayat AT
american.edu
I am a Professor of Mathematics at American University . I have been at AU since eternity (more precisely, 1987), except for my periods of sabbatical leave: I spent Fall 1993 in Tehran, Iran, as a faculty member at Sharif University of Technology, and a researcher at IPM ; and during Spring and Summer of 2007, I was in the Netherlands at Utrecht University .
I
grew up in Tehran, Iran, where I attended Ario Elementary School, and graduated from Alborz High School in 1976. I received my B.S. degree from Iowa State
University (1979), and my Ph.D. in Mathematics (1984) from the
University of Wisconsin (Madison), under
the direction of Ken
Kunen. I was a faculty member at Western Illinois University during 1984-1985, and at San Jose State University (California) during
1985-1987.
RESEARCH
I am a mathematical logician. My research is focused on models of set theory of all sorts, weak (fragments of ZF), strong (ZF with large cardinals), and bizarre (Quine-Jensen set theory NFU). I am also an enthusiast of models of arithmetic of various flavors, from fragments of PA, all the way to second order arithmetic and its subsystems.
One of my research projects deals with the comparative study of automorphisms of models of a variety of theories, ranging in strength from fragments of Peano arithmetic, all the way up to systems of set theory with large cardinals. The picture that has emerged from this work reveals that many foundational theories T (such as Peano arithmetic, second order arithmetic, and certain extensions of set theory with large cardinals) are characterized by the behavior of the automorphisms of models of T. This work also sheds light on the model theory of the Quine-Jensen system NFU of set theory with a universal set. I have completed four papers concerning automorphisms of models of foundational theories, available below, and I am working on-and-off on others.
I serve as an associate editor of the Bulletin of the Iranian Mathematical Society, dealing with papers in the areas of mathematical logic and set theory. You can find the latest issue of the Bulletin of the Iranian Mathematical Society online at http://bims.ims.ir .
Recent, and Not-so-Recent Talks
Kunen Fest: Topology and
Set Theory Conference (April 2009, University of Wisconsin, Madison), slides
CUNY Logic Workshop (Sep 2008, New York), slides
Mondriaanhuis (January
2008, Amersfoort, The Netherlands)
Amsterdam-Utrecht
Logic Colloquium (January
2008, Utrecht, The Netherlands)
CUNY Logic Workshop (October 2007, New York City)
CUNY
Models of PA Seminar (October 2007, New York City)
Bronx
Community College Mathematics Seminar (October
2007, Bronx, New York)
Amsterdam Set
Theory Meeting (August 2007,
Amsterdam, The Netherlands), slides
First
European Set Theory Conference
(July 2007, Bedlewo, Poland), slides
Sixth Panhellenic Logic Symposium (July 2007, Volos, Greece), slides
Fifty Years
of Generalized Quantifiers (June
2007, Warsaw, Poland), slides
IPM Logic Conference 2007
(June 2007, Tehran, Iran), slides(1), slides(2)
University of
Paris Logic Seminar (May 2007, Paris, France), slides
70th
Anniversary of NF (May 2007, Cambridge, England), slides
University
of Manchester Logic Seminar (April 2007, Manchester, England), slides
Oxford Logic
Seminar (April 2007, Oxford, England)
Amsterdam-Utrecht
Logic Colloquium (April 2007, Utrecht, The Netherlands), slides
Nonstandard
Methods and Applications (May
2006, Pisa, Italy)
CUNY Model Theory
Seminar (March 2006, New York City)
CUNY Logic Workshop (March 2006, New York City)
NYC Logic Conference (May 2005, New York City)
International
Congress M.ARI.AN. 2004 (June 2004, Pisa, Italy)
Mid-Atlantic
Mathematical Logic Seminar (April 2004,
Logic, Algebra, and Arithmetic (October 2003,
Upcoming Conferences
2nd European Set
Theory Meeting (July 2009, Bedlewo , Poland
Recent Conferences
Logic
Colloquium 2008 (July 2008, Bern ,
Switzerland
ASL Winter Meeting
(with Joint Mathematics Meetings) of the Association for Symbolic
Logic,
Kunen Fest: Topology and
Set Theory Conference (
Proceedings Volumes
Logic in Tehran, Proceedings of the Logic, Algebra, and
Arithmetic conference held in
Nonstandard Models of Arithmetic and Set Theory, Contemporary Mathematics, volume 361, American Mathematical Society (2004), edited by A. Enayat and R. Kossak, American Mathematical Society, Providence, RI, 2004.
Recent
Papers (PDF format)
Omega
Models of Finite Set Theory [with James Schmerl and Albert Visser], Utrecht
Logic Group Preprint Series, to appear in the Tennenbaum Memorial Volume (Lectures Notes in Logic, ASL and
Cambridge University Press).
A
Standard Model of Peano Arithmetic with No Conservative Elementary Extension, Annals
of Pure and Applied Logic, Vol. 156, Issues 2-3 (2008), pp. 308-318.
Model
Theory of the Regularity and Reflection Schemes [with Shahram
Mohsenipour], Archive
for Mathematical Logic, Vol. 47, #5 (2008), pp. 447-464.
Automorphisms
of Models of Arithmetic: A Unified View, Annals of Pure and Applied Logic, vol. 14, #1 (2007), pp.16-36.
Automorphisms of Models of Bounded Arithmetic,
Fundamenta Mathematicae, vol.192 (2006), pp. 37-65.
From Bounded Arithmetic to Second Order Arithmetic via Automorphisms, in Logic in Tehran, Lecture Notes in Logic, vol. 26, Association for Symbolic Logic, 2006.
Somewhat
Recent Papers (PDF format)
Automorphisms, Mahlo
Cardinals, and NFU, in Nonstandard
Models of Arithmetic and Set Theory Contemporary Mathematics, volume
361, American Mathematical Society, 2004.
Models of Set Theory with
Definable Ordinals, Archive for
Mathematical Logic, vol. 44, #3 (2005), pp. 363-385.
Leibnizian Models of Set
Theory, Journal of Symbolic Logic, vol. 69, # 3 (2004), pp. 775-789.
On the Leibniz-Mycielski
Axiom in Set Theory , Fundamenta
Mathematicae, vol. 181 (2004), pp.215-231.
Other
Published Papers
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Counting models of
set theory. Fund. Math. 174 (2002), no. 1, 23--47. Power like models
of set theory. J. Symbolic Logic 66 (2001), no. 4,
1766--1782.
d as a
continuous function of x and e. Amer. Math. Monthly 107 (2000), no. 2,
151--155. Analogues of the
MacDowell-Specker theorem for set theory. Models, algebras,
and proofs (Bogotá, 1995), 25--50, Lecture
Notes in Pure and Appl. Math., 203, Minimal elementary
extensions of models of set theory and arithmetic. Arch. Math. Logic 30 (1990), no. 3,
181--192. Undefinable
classes and definable elements in models of set theory and arithmetic. Proc. Amer. Math. Soc. 103 (1988), no.
4, 1216--1220 Conservative
extensions of models of set theory and generalizations. J. Symbolic Logic 51 (1986), no. 4,
1005--1021. Weakly compact
cardinals in models of set theory. J. Symbolic Logic 50 (1985), no. 2,
476--486. On certain
elementary extensions of models of set theory. Trans. Amer. Math. Soc. 283 (1984), no. 2,
705--715. (with A. Abian) Nonmetrizability
of uncountable well-ordered spaces. Simon Stevin 55 (1981), no. 1-2,
3--6. Ph.D. Students
1.
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