In what follows, we use small, upper case italic letters like \({\scriptsize A}, {\scriptsize B},\ldots\) as variables in \(\mathcal{L}_T\) ranging over sentences (or their Gödel numbers, to be precise). Thus \(\forall{\scriptsize A}(\ldots{\scriptsize A}\ldots)\) stands for \(\forall x(Sent_T (x) \rightarrow \ldots x\ldots)\), where \(Sent_T (x)\) expresses in the language of arithmetic that \(x\) is a sentence of the language of arithmetic extended by the predicate symbol \(T\). The syntactical operations of forming a conjunction of two sentences and similar operations can be expressed in the language of arithmetic. Since the language of arithmetic does not contain any function symbol apart from the symbol for successor, these operations must be expressed by sutiable predicate expressions. Thus one can say in the language \(\mathcal{L}_T\) that a negation of a sentence of \(\mathcal{L}_T\) is true if and only if the sentence itself is not true. We would write this as 