Degrees which do not bound minimal degrees

The high/low hierarchy respects the ordering of degrees, and so we can expect to find properties of order which are possessed by all degrees in a given hierarchy class. Such properties can also be found for classes of the generalized high/low hierarchy even though that hierarchy does not respect the ordering of the degrees. For example, Jockusch and Posner [4], extending a result of Cooper [l], showed that no degree in m is minimal. By results of Yates [S] and Sasso [7], this result is best possible as both GL1 and GL,? GL1 contain minimal degrees. Jockusch [3] showed that there is a degree in GL3 GL2 which does not bound a minimal degree, and conjectured that such a result should be true for all proper classes of the generalized high/low hierarchy except for GH,. We prove Jockusch’s conjecture in Section 1, and extend the result to the high/low hierarchy in Section 2. We will be using the following notation and definitions (see [5] for more detail). ( @e : e E N) is a