We present a theory of stratified truth ${\mathsf{ST}}_{\mu }$ with a μ‐operator, where terms representing fixed points of stratified monotone operations are available. We prove that ${\mathsf{ST}}_{\mu }$ is relatively intepretable into Quine's $\mathsf{NF}$ (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). The present version of ${\mathsf{ST}}_{\mu }$ is an enhancement of the theory presented in [2].

中文翻译：

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关于分层真理的不动点理论

我们提出了分层真理的理论 ${\mathsf{ST}}_{\mu }$使用μ运算符时，可以使用表示分层单调运算的固定点的项。我们证明${\mathsf{ST}}_{\mu }$ 相对于Quine来说是不可理解的 $\mathsf{NF}$（或其子系统）。这样做的动机是研究一个强大的真理理论，该真理理论通过分层即采用隐式类型理论学科是一致的，但在一定程度上却与自我参照兼容。当前版本${\mathsf{ST}}_{\mu }$ 是[2]中提出的理论的增强。