Prolegomena to the categorical study of interpretations

Albert Visser, University of Utrecht

Abstract: In this lecture we discuss some reasons for studying interpretations in a categorical framework. We illustrate that such categories are the natural home of Tarski's Theorem on the undefinability of Truth, an object-meta pair of theories being just a certain arrow in the category. As an application, we show that no extension of Peano Arithmetic (in the arithmetical language) can be isomorphic to an extension of Zermelo Fraenkel Set Theory (in the set theoretical language).