My primary areas of research are combinatorial set theory and category- theoretic logic. I have also worked in other areas of logic, in combinatorics, and in theoretical computer science.
Much of my set-theoretic work deals with families of subsets of N and families of functions N -> N, particularly the combinatorial aspects of ultrafilters and ultraproducts. I especially like set-theoretic problems that arise in other areas of mathematics. I am also interested in questions about the axiom of choice and weak forms of this axiom, as well as combinatorial properties of large cardinals. In category-theoretic logic, my main interest is the internal logic of topoi and its connection with geometric morphisms.
The following papers are fairly representative of my interests:
Applications of superperfect forcing and its relatives in Springer Lecture Notes in Math 1404 (ed. by J. Steprans & W.S. Watson).
Geometric invariance of existential fixed-point logic in Contemp. Math 92 (ed. by J. Gray & A. Scedrov).
Infinitary combinatorics and modal logic, J. Symbolic Logic 55 (1990) 761-778.
Existence of bases implies the axiom of choice in Contemp. Math. 31 (ed. by J. Baumgartner, D.A. Martin, and S. Shelah).
Many of my recent papers are available from my web page at http://www.math.lsa.umich.edu/~ablass via the links at the bottom of the page.