Joost Johannes Joosten

Title: Interpretability principles and logics for weak arithmetic theories

Abstract: In this talk we will speak on various aspects of interpretability
logics which are extensions of Gödel-Löb’s provability logic GL using a new
binary modality to model formalised interpretability. We will consider the
basic interpretability logic IL and various extensions where we shall be
interested both in modal as in arithmetical semantics. We will discuss some
history, some recent developments and some open questions. In particular, we
shall address the question on how to describe a collection of modal
interpretability principles that can be proven sound in any theory that
interprets Kalmar Elementary Arithmetic.