 Here \(T\) is the predicate intended to express truth and \(\langle \phi \rangle\) is a name for the sentence \(\phi\). Applying the predicate \(T\) to the name \(\langle \phi \rangle\) gives the expression \(T\langle \phi \rangle\) intended to represent the phrase “\(\phi\) is true”. Schema \(T\) thus expresses that for every sentence \(\phi , \phi\) holds if and only if the sentence “\(\phi\) is true” holds. The \(T\)-schema is usually regarded as a set of sentences within a formal theory. It is customary to use first-order arithmetic, that is, first-order predicate logic extended with a set of standard axioms for arithmetic like PA (Peano Arithmetic) or Robinson’s Q. What is being said in the following will apply to any such first-order formalisation of arithmetic. In this setting, \(\langle \phi \rangle\) above denotes the Gödel code of \(\phi\), and \(T\langle \phi \rangle\) is short for \(T(\langle \phi \rangle)\). The reader not familiar with Gödel codings (also known as Gödel numberings) can just think of the mapping \(\langle \cdot \rangle\) as a naming device or quotation mechanism for formulae—just like quotation marks in natural language. Often used notational variants for \(\langle \phi \rangle\) are \(\ulcorner \phi \urcorner\) and ‘\(\phi\)’.