The Settling Time Reducibility Ordering and {Delta}Formula Sets

The settling time reducibility ordering gives an ordering oncomputably enumerable sets based on their enumerations. The<_st ordering is in fact an ordering on c.e. sets, since itis independent of the particular enumeration chosen. In thisarticle, we show that it is not possible to extend this orderingin an approximation-independent way to sets in general, or even to n-c.e. sets for anyfixed n 3.