On classes of arithmetical counterparts of modal provability logics
A logic of provability \(\ell\) is defined as a modal logic which describes those principles of provability in Peano Arithmetic PA that can be demonstrated by means of a given theory T extending PA. In this situation T is called a counterpart of \(\ell\). Obviously, each logic of provability \(\ell\) has a smallest counterpart. The paper shows that a given logic of provability has a continuum of counterparts, each two of which are inconsistent. As a corollary we see that none of the logics of provability has a largest counterpart.
principles of provability in Peano Arithmetic
scientific article; zbMATH DE number 4168651
scientific article