Ali Enayat
CONTACT INFORMATION:
Department of Mathematics and
4400
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
I
grew up in Tehran , Iran Ario Elementary
School California
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Teaching
Materials for Calculus 1 (Summer 2008)
Syllabus, HW Set #1, HW Set #2, HW Set #3
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Research
I am a mathematical logician. My research is principally 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.
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 Netherlands
Amsterdam-Utrecht
Logic Colloquium (January 2008, Utrecht 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 Netherlands
First
European Set Theory Conference
(July 2007, Bedlewo , Poland
Sixth Panhellenic Logic Symposium (July 2007, Volos ,
Greece
Fifty Years
of Generalized Quantifiers (June
2007, Warsaw , Poland
IPM Logic Conference 2007
(June 2007,
University of
Paris Logic Seminar (May 2007,
70th
Anniversary of NF (May 2007,
University
of Manchester Logic Seminar (April 2007,
Oxford Logic
Seminar (April 2007,
Amsterdam-Utrecht
Logic Colloquium (April 2007,
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,
International
Congress M.ARI.AN. 2004 (June 2004, Pisa, Italy)
Mid-Atlantic
Mathematical Logic Seminar (April 2004,
Logic, Algebra, and Arithmetic (October 2003,
Proceedings Volumes
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
Papers (PDF format)
Omega
Models of Finite Set Theory [with James Schmerl and Albert Visser], Utrecht
Logic Group Preprint Series, to appear in the Tennenbaum Memorial Volume (ASL Lectures Notes).
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, to appear in the Annals of Pure and Applied Logic.
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
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
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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. 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
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