Certain truth predicates can be defined within the language of arithmetic. Predicates suitable as truth predicates for sublanguages of the language of arithmetic can be defined within the language of arithmetic, as long as the quantificational complexity of the formulas in the sublanguage is restricted. In particular, there is a formula \(Tr_0 (x)\) that expresses that \(x\) is a true atomic sentence of the language of arithmetic, that is, a sentence of the form \(n=k\), where \(k\) and \(n\) are identical numerals. For further information on partial truth predicates see, for instance, Hájek and Pudlak (1993), Kaye (1991) and Takeuti (1987).