Ali Enayat
e-mail : enayat AT american DOT edu
Telegraphic
Bio
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/research
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 ; I spent
September and October 2009 in Sweden at the Mittag-Leffler
Institute, and during November 2009 I was in the Netherlands for
collaborative work with Professor
Albert Visser at Utrecht University.
I
grew up in Tehran, Iran, where I attended Ario Elementary
School California
RESEARCH
I am a mathematical logician, with a strong interest in the metamathematics of foundational axiomatic systems such as Zermelo-Fraenkel set theory (ZF) and Peano arithmetic (PA).
My approach is dominantly model-theoretic and has focused on various types of set theory, weak (fragments of ZF), strong (ZF with large cardinals), and bizarre (Quine-Jensen set theory NFU); as well as arithmetical systems 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 several 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 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 .
Recent
Papers (PDF format)
An Improper Arithmetically Closed Borel Subalgebra of P(omega) mod FIN [with Saharon Shelah], to appear in Topology and Its Applications.
Omega Models of Finite Set Theory [with James Schmerl and Albert Visser], to appear in Set theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies (edited by J. Kennedy and R. Kossak), Cambridge University Press, to appear.
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
|
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, March 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 Talks
Pure Mathematics Seminar, University of
East Anglia (May, 2010, Model Theory Seminar, University of Leeds
(May, 2010, Logic Seminar, University of Manchester
(May, 2010, Somewhat Recent Talks
Mathematical
Institute of the University of Bonn (November 2009,
|
Recent Conferences
Logic
Colloquium 2008 (July 2008, Bern,
Switzerland)
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)
GRADUATE STUDENTS
Ph.D.
Students
·
Amir Togha, PhD George Washington University 2004, On Automorphisms
of Structures in Logic and Orderability of Groups in
Topology [jointly advised with Professor Valentina Harizanov]. Dr. Togha is currently an assistant professor at CUNY-Bronx.
·
Shahram Mohsenipour, PhD Institute for Theoretical Physics
and Mathematics (IPM) 2005, Elementary
End Extensions in Model Theory and Set Theory (Photos and Abstract ) Dr. Mohsenipour
is currently holding a postdoctoral position at IPM.
MA 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.
· Kun Zhao, (Laws of Large Numbers), completed Summer 2010.
· Adam Moskey (Contiunuous Selections), in progress.
· Michael Headley (Transcendental Numbers), in progress.