On the bounded quasi‐degrees of c.e. sets

Abstract

We study the degree structure of bQ-reducibility and we prove that for any noncomputable c.e. incomplete bQdegree a, there exists a nonspeedable bQ-degree incomparable with it. The structure D b s of the bs-degrees is not elementary equivalent neither to the structure of the be-degrees nor to the structure of the e-degrees. If c.e. degrees a and b form a minimal pair in the c.e. bQ-degrees, then a and b form a minimal pair in the bQ-degrees. Also, for every simple set S there is a noncomputable nonspeedable set A which is bQ-incomparable with S and bQ-degrees of S and A does not form a minimal pair.

On bQ1$bQ_1$‐degrees of c.e. sets

“…Proof In [10] it is proved that for any noncomputable c.e. $$bQ$$‐degree $$\mathbf {a}$$, there exists a nonspeedable $$bQ$$‐degree incomparable with it.…”

“…This paper is a natural continuation of [10]. In this paper we use simple sets to show some interesting properties of $${bQ}_1$$‐reducibility and $${bQ}_1$$‐degrees.…”