On a problem of G. E. Sacks
A. H. Lachlan · Proceedings of the American Mathematical Society · 1965
Introduction. On p. 171 of [2] Sacks asks whether there is an r.e. degree of unsolvability d which satisfies 0 (n) < d(n) < O(n+l) for all n. He also conjectures that a proof that such a d exists would use a combinatorial principle not touched on in [2]. In this paper we show using the methods of [2] that such a d exists.' Our proof assumes that the reader has a good understanding of [1] and of the proof of Theorem 3 [2, p. 86]. We present our construction in a semi-formal way in the hope that it will thus be made more comprehensible.