Ali Enayat

e-mail : enayat AT american DOT edu

 

 

Fall 2009 Whereabouts

I was on a research leave from AU during Fall 2009. I spent September and October in Sweden at the Mittag-Leffler Institute as a participant in the special program in mathematical logic. During November I was in the Netherlands for collaborative work with Professor Albert Visser at Utrecht University. I am scheduled to be back at AU for Spring 2010.

 

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 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 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.

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 .

 

 

Recent Papers (PDF format)

 

Omega Models of Finite Set Theory [with James Schmerl and Albert Visser],  to appear in Set theory, Arithmetic, Philosophy: Essays in Memory of Stanley Tennenbaum (edited by J. Kennedy and R. Kossak), Cambridge University Press, 2009/2010.

 

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.

 

Trees and Keisler's problem. Arch. Math. Logic 40 (2001), no. 4, 273--276.

 

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, Dekker, New York, 1999

 

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 Tehran during October 2003, edited by A. Enayat, I. Kalantari, and M. Moniri, Lecture Notes in Logic Series, vol. 26, Association for Symbolic Logic, La Jolla, CA; A K Peters, Ltd., Wellesley, MA, 2006.

 

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, Bonn, Germany), slides 

Mittag-Leffler Institute  (September 2009, Sweden),  slides 

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)

 Logic, Algebra, and Arithmetic  (October 2003, Tehran, Iran)

 

 

 

 

Recent Conferences

Logic Colloquium 2008 (July 2008, Bern, Switzerland)

ASL Winter Meeting (with Joint Mathematics Meetings) of the Association for Symbolic Logic, Washington, DC, Jan 7-8, 2009

 

Kunen Fest: Topology and Set Theory Conference (April 3-5 2009, University of Wisconsin, Madison)

 

 

 

FORMER 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.

M.S. 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.