University Seminar: Logic Across Disciplines-Can you always raise a natural number to a power? (Part 2)

Abstract:  We will continue our discussion of predicativity, the notion that we can only define new mathematical objects in terms of existing mathematical objects.  We will walk through the proofs of results by John Burgess and Allen Hazen, concerning how much of natural number arithmetic can be recovered in predicative second-order logic. In the final part of the talk, we will discuss potential avenues for future research extending Burgess’ and Hazen's work.