The settling time reducibility ordering and \({\Delta}_2^0\) sets. (English) Zbl 1163.03022

Csima, Barbara F.

J. Log. Comput. 19, No. 1, 145-150 (2009).

Summary: The settling time reducibility ordering gives an ordering on computably enumerable sets based on their enumerations. The \(<_{\text{st}}\) 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 \(\Delta_2^0\) sets in general, or even to \(n\)-c.e. sets for any fixed \(n \geq 3\).

MSC:

03D25

Recursively (computably) enumerable sets and degrees

Keywords:

computability theory; \({\Delta}^0_2\) sets; computable approximations