 Among the sentences that receive the value undefined in \(L_{\gamma}\) is the liar sentence. The solution to the liar paradox implicit in Kripke’s theory is this: Since both assuming that the liar sentence is true and that it is false leads to a contradiction it must be neither, it is undefined. The liar sentence is said to suffer from a truth-value gap. The idea of avoiding the liar paradox by allowing truth-value gaps did in fact appear several times in the literature before Kripke’s paper, but Kripke was among the first to make it an integral part of a genuine theory.