 For every degree \(\mathbf{a} \not\equiv_T \mathbf{0}\), there exists a degree \(\mathbf{b}\) which is incomparable to \(\mathbf{a}\)—i.e., \(\mathbf{b} \nleq_T \mathbf{a}\) and \(\mathbf{a} \nleq_T \mathbf{b}\). Moreover, there is a set of \(2^{\aleph_0}\) pairwise incompatible degrees (Kleene &amp; Post 1954).