 Note that if \(L_{\alpha}\) is one of the languages in Kripke’s construction, then \(L_{\alpha +1} = \tau(L_{\alpha})\). The idea of this truth revision operator \(\tau\) is that if \(\tau(L)=L'\) then \(L'\) will be a language in which \(T\) is interpreted as the truth predicate for \(L\). If therefore \(\tau(L)=L\) for some \(L\), that is, if \(L\) is a fixed point of \(\tau\), then \(L\) will be a language containing its own truth predicate. This motivates the search for fixed points of \(\tau\). Since \(\tau\) is easily seen to be monotone, by the fixed point theorem it has a least fixed point. It is not hard to see that this fixed point is exactly the language \(L_{\gamma}\) constructed in Kripke’s theory of truth. Kripke’s construction is thus recaptured in the setting of fixed points for monotone operators.