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 during the ancien régime, 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 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.
The first draft of a joint paper with Albert Visser of full satisfaction classes in a general setting will soon appear here.
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
An improper arithmetically closed Borel subalgebra of P(omega) mod FIN [with Saharon Shelah], Topology and Its Applications, to appear (online journal copy available here).
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, 2011.
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
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 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,
Conservative
extensions of models of set theory and generalizations.,J. Symbolic Logic, 51 (1986), no. 4,
pp. 1005-1021.
Weakly compact cardinals in models of set
theory, Journal
of Symbolic Logic, 50 (1985), no. 2,
pp. 476-486.
On certain elementary extensions of models of set theory. Transactions of American Mathematical Society, 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.
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, 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
CUNY Logic Workshop
(April 2011, New York City)
Young
Set Theory Workshop, (March 2011, Königswinter, Germany), slides
1, slides
2 Somewhat
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,
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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 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.
· Amanda Purcell (thesis topic: Set Theory), in progress.
· Michael Cassel (thesis topic: Model Theory), in progress.