  We introduce a tool for analysing models of $\textnormal{CT}^-$, the
compositional truth theory over Peano Arithmetic. We present a new proof of
Lachlan's theorem that arithmetical part of models of $\textnormal{PA}$ are
recursively saturated. We use this tool to provide a new proof that all models
of $\textnormal{CT}^-$ carry a partial inductive truth predicate. Finally, we
construct a partial truth predicate defined for formulae from a nonstandard cut
which cannot be extended to a full truth predicate satisfying
$\textnormal{CT}^-$.
