# The logic of the Gödel proof predicate

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## Abstract

We discuss the logics of the operators “p is a proof of *A*” and “*p* is a proof containing A” for the standard Gödel proof predicate in Peano Arithmetic. Decidability and arithmetical completeness of these logics are proved. We use the same semantics as for the Provability Logic where the operator “*A* is provable” is studied.

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© Springer-Verlag Berlin Heidelberg 1993