The Kripke–Feferman theory retains the truth iteration axiom \(\forall{\scriptsize A}(T[T{\scriptsize A}] \leftrightarrow T{\scriptsize A})\), but the notion of truth axiomatized is no longer classical because the negation axiom \(\forall{\scriptsize A}(T[\neg{\scriptsize A}] \leftrightarrow \neg T{\scriptsize A})\) is dropped. 