Date: February 21, 2014 Venue: Sendai Logic School, Tokyo Institute of Technology Speaker: Stephen G. Simpson Title: Reverse mathematics and Hilbert's program (a 1-hour tutorial for graduate students) Abstract: I will make some remarks concerning reverse mathematics and its application to Hilbert's foundational program of finitistic reductionism. My thesis is that, in order for a piece of mathematics to be finitistically reducible, its proof-theoretic strength must be no greater than that of PRA (= Primitive Recursive Arithmetic). Reverse Mathematics has been very useful for determining which theorems are reducible to PRA in this sense. I will mention some old and new theorems of this kind.