Countable initial segments of the degrees of unsolvability
A. H. Lachlan, R. Lebeuf · Journal of Symbolic Logic · 1976
In this paper we show that any countable upper semilattice with zero can be embedded as an initial segment of the degrees of unsolvability. This provides a characterization of the order types of the countable initial segments of the degrees since any such initial segment is trivially an initial segment of a countable upper semilattice. Let a segment S of the degrees be a set of degrees such that, if a, b Є S and a < c < b, then c Є S. One may readily observe that our result also characterizes the order types of all countable segments of the degrees of unsolvability.