Structural properties of Q -degrees of n-c. e. sets

Abstract In this paper we study structural properties of n-c. e. Q -degrees. Two theorems contain results on the distribution of incomparable Q -degrees. In another theorem we prove that every incomplete Π 2 0 Q -degree forms a minimal pair in the c. e. degrees with a Δ 2 0 Q -degree. In a further theorem it is proved that there exists a c. e. Q -degree > 0 that is not half of a minimal pair in the c. e. Q -degrees.