On the r.e. predecessors of d.r.e. degrees

Abstract

Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets ) and R[d] be the class of less than d r.e.degrees in which d is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d R[d] is not empty. We show that the r.e.degree defined by Lachlan for a d.r.e.set D ∈d is just the minimum degree in… (More)
DOI: 10.1007/s001530050132

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