The Settling Time Reducibility Ordering and Δ02 Sets

The settling time reducibility ordering gives an ordering on computably enumerable sets based on their enumerations. The <st ordering is in fact an ordering on c.e. sets, since it is independent of the particular enumeration chosen. In this article, we show that it is not possible to extend this ordering in an approximation-independent way to Δ⁰2 sets in general, or even to n-c.e. sets for any fixed n ≥ 3.