 For any c.e. degree \(\mathbf{a} &gt;_T \mathbf{0}\), there are incomparable c.e. degrees \(\mathbf{b},\mathbf{c} &lt;_T \mathbf{a}\) such that \(\mathbf{a} = \mathbf{b} \cup \mathbf{c}\) (Sacks 1963b).