Provability logic is a branch of mathematical logic that studies formal systems of provability. Specifically, it deals with the properties and behaviors of provability predicates, which are statements or operators that express the idea that a certain statement is provable within a given formal system. One of the most prominent systems within provability logic is known as Gödel's provability logic, often represented by the modal system \( GL \) (Gödel-Löb logic).
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