The basic theorems of Provability Logic arethree in number. First is the Arithmetical Completeness
Theorem. The second place is shared by the theorems affirming the Uniqueness of Fixed Points and
the Explicit Definability of Fixed Points. In this paper we consider the problem of Uniqueness and:
Explicit Definability of Fixed Points for Interpretability Logic. It turns out that Uniqueness is an
immediate corollary of a theorem of Smoryriski, so. most of the paper, is devoted to proving Explicit
Definability
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