 From a proof-theoretic perspective \(\mu\)KF is significantly stronger than KF. The single axiom schema expressing the minimality of the truth predicate allows one to embed into \(\mu\)KF the system ID\(_1\) of one arithmetical inductive definition, an impredicative theory. While intuitively plausible, \(\mu\)KF suffers the same expressive incompleteness as KF: Since the minimal Kripkean fixed point forms a complete \(\Pi^{1}_1\) set and the internal theory of \(\mu\)KF remains recursively enumerable, there are standard models of the theory in which the interpretation of the truth predicate is not actually the minimal fixed point. At present there lacks a thorough analysis of the models of \(\mu\)KF. 