An axiomatic approach to self-referential truth

Abstract We add a new predicate T to the language of Peano Arithmetic, with T(x) intended to mean ‘x is the Godel number of a true sentence of the augmented language’. We create a list of plausible axioms and rules of inference concerning this predicate T, each of which embodies some aspect of its intended interpretation as truth. We classify all subsets of the list as either consistent or inconsistent, and we measure the proof-theoretic strength of several subsets by comparing them with familiar systems of arithmetic and analysis.