On a question of G. E. Sacks

Abstract

In [1], p. 171, Sacks asks (question (Q5)) whether there is a recursively enumerable degree of unsolvability d such that for all n ≧ 0. Sacks points out that the set of conditions which d must satisfy is not arithmetical. For this reason he suggests that a proof of (Q5) might require some new combinatorial device. The purpose of this note is to show how (Q5) may be proved simply by extending the methods of [l].2