Minimal \(m\)-powers (Q1280646)

A PRF (partial recursive function) \(f\) has minimal \(m\)-power if (1) \(\text{ dom}(f)\) is not recursive; and (2) if \(g\) is a PRF such that \(\text{ dom}(g)\) is not recursive, \(\text{ rang}(f) = \text{ rang}(g)\) and \(g\leq_m f\), then \(f\leq_m g\). This note shows a necessary and sufficent condition for a PRF to have minimal \(m\)-power.