The provability logics of recursively enumerable theories extending Peano arithmetic at arbitrary theories extending Peano arithmetic (Q1068069)

We fully characterize the provability logics of RE theories T extending PA at PA and at T. We show that ''nearly all'' provability logics of RE theories T extending PA at arbitrary U extending PA are between Löb's logic L and Solovay's logic S. At the end of the paper we take a brief look at what goes on between L and S. We give examples of new phenomena there.