Department of Mathematics, I. Javakhishvili Tbilisi State University, 13, University Str., Tbilisi 0186, Georgia
Abstract:
We study the degree structure of bQ‐reducibility and we prove that for any noncomputable c.e. incomplete bQ‐degree a, there exists a nonspeedable bQ‐degree incomparable with it. The structure $mathcal {D}_{mbox{bs}}$ of the $mbox{bs}$‐degrees is not elementary equivalent neither to the structure of the $mbox{be}$‐degrees nor to the structure of the $mbox{e}$‐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.