Office: 3830 East Hall
Mathematics Department
University of Michigan
(2074 East Hall
530 Church St.)
Ann Arbor, MI 48109-1043
U.S.A.
Office phone: (734) 763-1183
Dept. fax: (734) 763-0937
Research
My research is primarily in mathematical logic, especially set theory, but it extends into other areas, including finite combinatorics, category theory, and theoretical computer science. Here are some of the subjects I’ve worked in recently.
- Set theory
- Infinitary combinatorics, especially ultrafilters on the natural numbers
- Cardinal characteristics of the continuum
- Applied set theory, especially in abelian group theory
- Category theory
- Topoi and their internal logic
- Logic of geometric morphisms
- Finite combinatorics
- Theoretical computer science
- Complexity theory
- Applications of mathematical logic
- Linear logic
- Game semantics
- Connection with cardinal characteristics
Administration
I am associate chairman for regular faculty appointments.
My term as associate chairman for graduate studies ended in August, 1999. The present holder of that office is Professor Sergey Fomin, whose e-mail address for administrative matters is [email protected]
Links to Papers
The following links will take you to pages on which my recent papers are listed with abstracts and links to PostScript and PDF files of the papers themselves. “Recent” is defined as “existing in electronic form”; the borderline between recent and archaic is roughly 1993, with several exceptions. Dave Childs has generously provided an electronic version of my 1984 paper “The interaction between category theory and set theory” and Peter Krautzberger has done the same for my 1978 paper “A model-theoretic view of some special ultrafilters” and my 1987 paper “Ultrafilters related to Hindman’s finite-unions theorem and its extensions.” Finally, a scanned copy of my 1970 Ph.D. thesis (rather outdated by now) is available here (and on the set theory page below).
Topos Theory and Constructive Logic
Theoretical Computer Science
Linear Logic and Game Semantics
Finally, although I don’t do partial differential equations, my son Timothy does
About Me
My recent research is in set theory, topos theory, and theoretical computer science. In set theory, I work on cardinal characteristics of the continuum, ultrafilters and ultraproducts, and the axiom of choice and its consequences. In topos theory, I work primarily on the internal logic, especially as it relates to classifying topoi and to the axiom of choice. In computer science, part of my work is of a general foundational nature, and part is connected with quantum computation, especially the theory of anyons. I have also worked in finite combinatorics.
