 As is easily shown to be true of the join operation \(\mathbf{a} \vee \mathbf{b}\), the jump operation \(\mathbf{a}' = \mathbf{b}\) is definable in \(\mathcal{D}_T\) in the language with \(\equiv_T\) and \(\leq_T\) (Shore &amp; Slaman 1999).