An explicit basis for the admissible inference rules in the Gödel–Löb logic $GL$

We describe an explicit basis for the admissible inference rules in the Gödel–Löb logic. The basis consists of a sequence of inference rules in infinitely many variables. Inference rules in the reduced form play an important role in this study. Alongside a basis for the admissible rules we obtain a basis for the quasi-identities of the countable rank free algebra in the Gödel–Löb logic.