Ali Enayat

e-mail : enayat AT american DOT edu






Ali at the board

Telegraphic Bio

I started working as a faculty member in the Department of Mathematics and Statistics of American University in 1987, and have been here 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 during the ancien régime, where I attended Ario Elementary School, and graduated from Alborz High School  in 1976, three years before the Iranian revolution. 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.



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 fragments of ZF, ZF with large cardinals, Quine-Jensen set theory NFU, and arithmetical systems of various flavors, ranging 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 calibrating the interpretability strength of various foundational systems (including finite set theory, and theories with built-in satisfaction classes). 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.

My latest work involves a new look at self-embeddings of models of arithmetic and set theory. Some of this work is in collaboration with Volodya Shavrukov.

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 .


Recent Papers :

 New Constructions of full satisfaction classes (with Albert Visser).

Also, the paper below is ready; send me an e-mail if you are interested in obtaining a copy:

A New Proof of Tanaka’s Theorem (every nonstandard countable model of WKL0  has a nontrivial self-embedding onto an initial segment of itself).

·        Models of Arithmetic Papers

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.

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.

·        Models of Set Theory AND Arithmetic Papers

Omega-models of finite set theory [with James Schmerl and Albert Visser], in Set theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies (edited by J. Kennedy and R. Kossak), Cambridge University Press, 2011.


An improper arithmetically closed Borel subalgebra of P(omega) mod FIN [with Saharon Shelah], Topology and Its Applications, December 2011, pp. 2495-2502,  journal copy available here.



Minimal elementary extensions of models of set theory and arithmetic,  Archive for Mathematical Logic, (1990), no. 3, 181-192. 


Undefinable classes and definable elements in models of set theory and arithmetic. Proceedings of American Mathematical Society, 103 (1988), no. 4, 1216-1220

·        Models of Set Theory Papers

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.

Counting models of set theory. Fundamenta Mathematicae vol. 174 (2002), no. 1, pp. 23-47.


Power-like models of set theory, Journal of Symbolic Logic  (2001), no. 4, pp. 1766-1782.


Analogues of the MacDowell-Specker theorem for set theory. Models, algebras, and proofs (Bogotá, 1995), pp. 25-50, Lecture Notes in Pure and Appl. Math., 203, Dekker, New York, 1999.


Conservative extensions of models of set theory and generalizations.,J. Symbolic Logic, vol. 51 (1986), no. 4, pp. 1005-1021.


Weakly compact cardinals in models of set theory, Journal of Symbolic Logic,  vol. 50 (1985), no. 2, pp. 476-486.


On certain elementary extensions of models of set theory. Transactions of American Mathematical Society, vol. 283 (1984), no. 2, pp. 705-715.


·        General Model Theory Papers

Model Theory of the Regularity and Reflection Schemes [with Shahram  Mohsenipour],  Archive for Mathematical Logic, Vol. 47, #5 (2008), pp. 447-464.


Trees and Keisler's problem, Archive for Mathematical Logic, 40 (2001), no. 4, pp. 273-276.

·        Topology Papers

Delta as a continuous function of x and epsilon. American Mathematical Monthly, 107 (2000), no. 2, pp. 151-155.


 Nonmetrizability of uncountable well-ordered spaces [with A. Abian], Simon Stevin (published in Belgium) 55 (1981), no. 1-2, pp. 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 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, vol. 361, American Mathematical Society (2004), edited by A. Enayat and R. Kossak, American Mathematical Society, Providence, RI, 2004.


·       Forthcoming 2013 Meetings

Nordic Spring School in Logic 2013, Nordfjordeid, Norway, May 27-31.

Swedish Congress of Philosophy, Stockholm,June 14-16.

32nd Weak Arithmetics Days, June 24-26, Athens, Greece.

 Sy David Friedman's 60th-Birthday Conference, Vienna, Austria, July 8-12.


 Fourth European Set Theory Conference, Barcelona, Spain, July 15-18.


 Proof Theory in Lisbon, Portugal, July 19.


 Logic Colloquium 2013, Evora, Portugal, July 22-27.


·       Recent Talks, Visits, and Meetings

University of Oslo Logic Seminar (Norway, Sep 13, 2012)


 University of Gothenburg Logic Seminar (Sweden, Sep 14, 2012)

Oxford, UK ( March 26-28, 2012, visited Prof. Volker Halbach and his research group)

Cambridge, UK (March 28-30, 2012, visited Prof. Thomas Forster and his research group)

CUNY Models of Arithmetic Seminar  (May 2012, New York)

15th Latin American Symposium on Mathematical Logic (June 2012, Bogota,  Colombia)

Model Theory and Proof Theory of Arithmetic; A Memorial Conference in Honour of H. Kotlarski and Z. Ratajczyk  (July 2012, Bedlewo,  Poland)


·       Somewhat Recent Talks

CUNY Logic Workshop  (April 2011, New York City)

Young Set Theory Workshop, (March 2011, Königswinter, Germany), slides 1, slides 2


·       Less Recent Talks

Pure Mathematics Seminar, University of East Anglia  (May, 2010, Norwich, England)


Model Theory Seminar, University of Leeds  (May 2010, Leeds, England)


Logic Seminar, University of Manchester  (May 2010, Manchester, England)

Mathematical Institute of the University of Bonn  (November 2009, Bonn, Germany), slides

Lisbon Logic Group (November 2009, Lisbon, Portugal)

Mittag-Leffler Institute  (September 2009, Djursholm, 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)




Model Theory and Proof Theory of Arithmetic. A Memorial Conference in Honour of H. Kotlarski and Z. Ratajczyk (July 2012, Bedlewo, Poland)


ASL Winter Meeting (with Joint Mathematics Meetings) of the Association for Symbolic Logic (January 2009, Washington, DC)


Logic Colloquium 2008 (July 2008, Bern, Switzerland) 




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. Dr. Mohsenipour is currently holding a research position at IPM.


MA Students


Betsy Andersen (project topic: Coding Theory), completed Spring 1994.

Omar Mirza (project topic: Gödel’s Theorem), completed Summer 1994.

Blair Jones, (thesis topic: Ramsey Theory), completed Spring 1995.

Michelle Perschbacher (project topic: Music and Number Theory), completed Summer 1997.

Valbona Bejleri (project topic: The Probablistic Method), completed Summer 2001.

Adeniran Adeboye (project topic: Combinatorial Number Theory), completed Spring 2002.

Anna Rose Haralampus (project topic: Fractals and Topology), completed Spring 2003.

Caleb Rossiter (thesis topic: Relativity Theory), completed Spring 2004.

Stephen Wheatley (project topic: Nonstandard Analysis), completed Spring 2006.

Mahmoud Momenipour IASBS  (thesis topic: Logical Foundations of Nonstandard Analysis), completed Fall 2006.    

Kun Zhao, (project topic: Laws of Large Numbers), completed Summer 2010.

Adam Moskey (thesis topic: Continuous Selections), completed Fall 2010.

Michael Headley (project topic: Transcendental Numbers), completed Fall 2010.

Michael Cassel (project topic: Automorphisms of Models of PA), completed, Spring 2013.

Amanda Purcell (thesis topic: Ultraproducts and Applications), in progress.