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

Abstract:  We will discuss predicativity, the notion that we can only define new mathematical objects in terms of existing mathematical objects.  We will give an introduction to second-order logic, and explain how we can use it to do mathematics predicatively.  In the final portion of the talk, we will discuss work by John Burgess and Allen Hazen concerning how much of Peano arithmetic is predicatively justifiable.