 In the case of  Theorem 3.8,  this technique is used to simultaneously construct the two c.e. sets \(A\) and \(B\) of degree intermediate between \(\mathbf{0}\) and \(\mathbf{0}'\) by alternating between the requirements \(R_{2i}\) which entail that \(A \neq \{n : \phi^{B}_i(n) \darrow = 1\}\) at even stages to ensure \(A \nleq_T B\) and requirements \(R_{2i+1}\) which entail that \(B \neq \{n : \phi^{A}_i(n) \darrow = 1\}\) at odd stages so as to ensure \(B \nleq_T A\).