Ali Enayat

 

CONTACT INFORMATION:

 

Department of Mathematics and Statistics
American University
4400 Mass. Ave. NW
Washington, DC 20016-8050

USA

e-mail : enayat AT american.edu

I am a Professor of Mathematics at American University . I have been at AU since 1987 except for my periods of sabbatical leave: during Fall 1993 I was a faculty member at Sharif University of Technology, and a researcher at IPM in Tehran, and during Spring and Summer of 2007, I was at  Utrecht University in the Netherlands.

I grew up in Tehran, Iran, where I attended Ario Elementary School, and Alborz High School . 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.

 

Current Teaching Materials (Spring 2008)

Finite Mathematics (Math 150.001): 

Assignment Sets: #1, #2, #3

Syllabus, Solutions to Q1, Solutions to Q2, Solutions to Quiz 3  (in-class + take-home), Solutions to Quiz 4,  Solutions to Exam 1, Solutions to Quiz 5, Solutions to Quiz 6 (in-class + take-home), Solutions to Q7, Solutions to Q8, Solutions to Exam 2, Solutions to Q9, Solutions to Q10, Solutions to Q11

Modern Algebra II (Math 513.001):

 Syllabus, Assignment 1, Assignment 2, Assignment 3, Assignment 4,  Assignment 5, Assignment 6, Assignment 7, Assignment 8

Notes: Group Theory Review, Solutions to Group Theory Review, Notes on Reducibility, Notes on Number Theory, Notes on Field Theory

Exam -1: Review + Review -Solutions  + The real exam + Solutions

Exam-2: Review + The real exam + Solutions

 

Research

I am a mathematical logician. My research is principally focused on models of set theory and arithmetic, but I have an interest in many areas of mathematical logic, especially those dealing with foundational issues.

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 under “recent papers” (with more to follow).

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 Talks/ Conferences

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, Washington, D.C.)

 

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

 

 

 

Proceedings Volumes

 

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 Papers (PDF format)

Omega-Models of Finite Set Theory  [with James Schmerl and Albert Visser], preprint.

Model Theory of the Regularity and Reflection Schemes [with Shahram Mohsenipour],  To appear in Archive for Mathematical Logic.

A Standard Model of Peano Arithmetic with No Conservative Elementary Extension, preprint.

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, the proceedings of the workshop and conference Logic, Algebra, and Arithmetic, held in Tehran, Iran, during October 2003, Lecture Notes in Logic, vol. 26, ASL and A. K. Peters, 2006.

 

Somewhat Recent Papers (PDF format)

Automorphisms, Mahlo Cardinals, and NFU, in Nonstandard Models of Arithmetic and Set Theory (edited by Ali Enayat and Roman Kossak), 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.

 

 

 

Ph.D. Students

1.      Amir Togha, PhD George Washington University 2004, On Automorphisms of Structures in Logic and Orderability of Groups in Topology [jointly advised with V. Harizanov]. Dr. Togha is currently an assistant professor at CUNY-Bronx.

2.      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

1. Betsy Andersen (Coding Theory), completed Spring 1994.

2. Omar Mirza (Gödel’s Theorem), completed Summer 1994.

3. Blair Jones, (Ramsey Theory), completed Spring 1995.

4. Michelle Perschbacher (Music and Number Theory), completed Summer 1997.

5. Valbona Bejleri (The Probablistic Method), completed Summer 2001.

6. Adeniran Adeboye (Combinatorial Number Theory), completed Spring 2002.

7. Anna Rose Haralampus (Fractals and Topology), completed Spring 2003.

8. Caleb Rossiter (Relativity Theory), completed Spring 2004.

9. Stephen Wheatley (Nonstandard Analysis), completed Spring 2006.

10. Mahmoud Momenipour IASBS  (Logical Foundations of Nonstandard Analysis), completed Fall 2006.                                                                                                                                                                                                                                                                                                               

 

 

**********************************************************************

 

Link of interest for logicians: Mathematical Logic around the world

 

Back to the department homepage:  American University Math/Stat Department