Visser (1989) has studied non-wellfounded hierarchies of languages and axiomatizations thereof. If one adds the \(T\)-sentences \(T_n\ulcorner \phi \urcorner \leftrightarrow \phi\) to the language of arithmetic where \(\phi\) contains only truth predicates \(T_k\) with \(k\gt n\) to PA, a theory is obtained that does not have a standard \((\omega\)-)model.