The modal logic of Gödel sentences (Q600852)

A Gödel sentence is a PA-unprovable sentence of the language of PA which is true in the standard model of the natural numbers. In the style of provability logics, the author presents here a modal logic GS for such Gödel sentences. He proves a Kripke-style completeness theorem, gives mutually faithful interpretations for GS with the provability logics GL and Grz and also with intuitionistic logic. And he proves an arithmetic completeness theorem saying that the arithmetical interpretations of GS-sentences are just the ``true but unprovable'' Gödel sentences of arithmetic.