Characters and fixed-points in provability logic.

Abstract

Some basic theorems about provability logic -the system of modal logic that reflects the behavior of formalized provability predicates in theories such as arithmetic -are given simplified, model-theoretic proofs. The theorems include the Fixed Point Theorem of de Jongh and Sambin, the Craig Interpolation Theorem, and the Beth Definability Theorem. Attention is also paid to the complexity of models for formulas in this logic.