 There are continuum (i.e., \(2^{\aleph_0}\)) many distinct Turing degrees. In particular, although for a given degree \(\mathbf{a}\) the set of \(\mathbf{b}\) such that \(\mathbf{b} \leq_T \mathbf{a}\) is countable, the set of \(\mathbf{b}\) such that \(\mathbf{a} &lt;_T \mathbf{b}\) is uncountable (Kleene &amp; Post 1954).