Abstract

In this paper, we establish a relationship between the join property and Turing degrees of members of effectively closed sets in Cantor space, i.e., classes. We first give a proof of the observation that there exists a non‐empty special class in which no join of two members computes the halting set. We then prove the existence of a non‐empty special class such that no member satisfies the join property, where a degree satisfies the join property if for all non‐zero there exists such that.