An overview of Interpretability Logic

Abstract

A miracle happens. In one hand we have a class of marvelously complex theories in predicate logic, theories with 'sufficient coding potential', like PA (Peano Arithmetic) or ZF (Zermelo Fraenkel Set Theory). In the other we have certain modal propositional theories of striking simplicity. We translate the modal operators of the modal theories to certain specic, fixed, defined predicates of the predicate logical theories. These special predicates generally contain an astronomical number of symbols. We interpret the propositional variables by arbitrary predicate logical sentences. And see: the modal theories are sound and complete for this interpretation. They codify precisely the schematic principles in their scope. Miracles do happen ....