Two Perspectives on Recursion and Induction: Modal Provability Logic and Fixed-Point Logics

Recursion and induction are ubiquitous logical mechanisms. I will compare two styles of dealing with them: one based on well-founded orderings and one on general fixed-point logics, showing that the two are connected in interesting ways. I present some theorems and conjectures to this effect, and if time permits, I will also point out some implications of this theme for discussions of ‘logical constants’ in the philosophy of logic.