Ali Enayat

I was on a research leave from
AU during Fall 2009. I spent September and October in
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 ; during Spring and Summer of 2007, I was in the Netherlands at Utrecht University ; and currently I am on a research leave in Northern Europe (see above).
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.
More recently, I have also started working on the metamathematics of finite set theory, with an eye towards calibrating the interpretability strength of various systems of finite set theory. My joint paper with Albert Visser and James Schmerl (available below) is the first paper in a projected series of papers dealing with this topic.
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 .
Omega Models of Finite Set Theory
[with James Schmerl
and Albert Visser], to appear in Set theory, Arithmetic, Philosophy: Essays
in Memory of
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.
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. Edited
Proceedings Volumes Proceedings of the IPM Logic Conference 2007, Special Issue of the Annals of Pure and Applied Logic, (guest) edited by A. Enayat and I. Kalantari, to appear in 2009/2010. 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, and Not-so-Recent Talks
Mathematical
Institute of the University of Bonn (November 2009,
|
ASL Winter Meeting
(with Joint Mathematics Meetings) of the Association for Symbolic Logic,
Washington, DC,
Kunen
Fest: Topology and Set Theory Conference (April 3-5 2009, University of
Wisconsin, Madison)
FORMER GRADUATE STUDENTS
· Betsy Andersen (Coding Theory), completed Spring 1994.
· Omar Mirza (Gödel’s Theorem), completed Summer 1994.
· Blair Jones, (Ramsey Theory), completed Spring 1995.
· Michelle Perschbacher (Music and Number Theory), completed Summer 1997.
· Valbona Bejleri (The Probablistic Method), completed Summer 2001.
· Adeniran Adeboye (Combinatorial Number Theory), completed Spring 2002.
· Anna Rose Haralampus (Fractals and Topology), completed Spring 2003.
· Caleb Rossiter (Relativity Theory), completed Spring 2004.
· Stephen Wheatley (Nonstandard Analysis), completed Spring 2006.
· Mahmoud Momenipour IASBS (Logical Foundations of Nonstandard Analysis), completed Fall 2006.