In many axiomatic truth theories, truth is taken as a predicate applying to the Gödel numbers of sentences. Peano arithmetic has proved to be a versatile theory of objects to which truth is applied, mainly because adding truth-theoretic axioms to Peano arithmetic yields interesting systems and because Peano arithmetic is equivalent to many straightforward theories of syntax and even theories of propositions. However, other base theories have been considered as well, including formal syntax theories and set theories.