A fixed point theory over stratified truth

We present a theory of stratified truth STm with a $mu$-operator, where terms representing fixed points of stratified monotone operations are available. We prove that STm is relatively intepretable into Quine's NF (or subsystems thereof). The motivation is to investigate a strong theory of truth, which is consistent by means of stratification,, i.e. by adopting an implicit type theoretic discipline, and yet is compatible with self-reference (to a certain extent).