The above mentioned theories of truth can be iterated by introducing indexed truth predicates. One adds to the language of PA truth predicates indexed by ordinals (or ordinal notations) or one adds a binary truth predicate that applies to ordinal notations and sentences. In this respect the hierarchical approach does not fit the framework outlined in Section 2, because the language does not feature a single unary truth predicate applying to sentences but rather many unary truth predicates or a single binary truth predicate (or even a single unary truth predicate applying to pairs of ordinal notations and sentences).