 This shows that \(L_{\gamma}\) is actually a language containing its own truth predicate: Any sentence \(\phi\) is true (false) if and only if the sentence expressing its truth, \(T\langle \phi \rangle\), is true (false). The equivalence (5) is nothing more than a semantic analogue of Tarski’s schema \(T\) in a three-valued setting. The construction of the language \(L_{\gamma}\) was one of the major contributions of Kripke (1975). It shows that in a three-valued logical setting it is actually possible for a language to contain its own truth predicate. It is easy to see that the third value, undefined, is essential to making things work: If \(L_{\gamma}\) had been a totally interpreted language (that is, a language with no undefined sentences), then \(L_{\gamma}\) would satisfy schema T, by (5) above. However, it immediately contradicts Tarski’s theorem that such a totally interpreted language can exist.