[Revised entry by Rineke (L.C.) Verbrugge on March 4, 2024.
Changes to: Main text, Bibliography, notes.html]
Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates. The logic has been inspired by developments in meta-mathematics such as Godel’s incompleteness theorems of 1931 and Lob’s theorem of 1953. As a modal logic, provability logic has been studied since the early seventies, and has had important applications in the foundations of mathematics….

Originally appeared on Stanford Encyclopedia of Philosophy Read More