FOM: Alternative foundations for mathematics

[Jesse A. Alama]

Often times when people talk about "foundations of mathematics", they
mean "set theory and its extensions".  I'm particularly interested in
finding out more on "alternative" foundations for mathematics, by
which I mean programs which do not intrinsically hinge upon set
theory (e.g., ZF).  In particular, I am familiar with illative combinatory
logic (the development of which, Curry thought, would provide an
alternative foundation for mathematics); but what other directions are
researchers in foundations taking besides set-theoretical ones?

Warm regards,



Jesse Alama
University of Minnesota, Morris
alamaja at mrs.umn.edu