Structural properties of \(Q\)-degrees of n-c.e. sets (Q958482)

In the paper structural properties of n-c.e. \(Q\)-degrees are studied. Some results on the distribution of incomparable \(Q\)-degrees are proved. It is also proved that: (1) every incomplete \(\Pi^{0}_{2}\) \(Q\)-degree forms a minimal pair in the c.e. degrees with a \(\Delta^{0}_{2}\) \(Q\)-degree. and (2) there exists a c.e. \(Q\)-degree \(> {\mathbf 0}\) that is not half a minimal pair in the c.e. \(Q\)-degrees.