 Intuitively, \(\TRUE^N\) is the set of those natural numbers that are Gödel numbers of true arithmetic sentences of vocabulary \(\tau\); and \(\psi(x)\) says that \(x\) is a Gödel number in the extension of the predicate \(\TRUE\). The formula \(\psi(x)\) is a conjunction including clauses that mimic, on the object-language level, the metalogical recursive clauses of the Tarski-type truth-definition for \(\mathbf{FO}\). E.g., one of the conjuncts is