 Upon examination, however, it is clear that the only features of a model of computation on which the proof of  Theorem 3.5  relies are the existence of an indexation for which a version of the  s-m-n Theorem (3.1)  is available. If \(\mathbf{M}\) satisfies these conditions, the claim that \(h(y)\) is computable relative to \(\mathbf{M}\) is equivalent to \(h(y) \simeq \phi_n(y)\) where \(n\) is an index drawn from some suitable indexation of the \(\mathbf{M}\)-computable functions. But since the s-m-n Theorem for \(\mathbf{M}\) allows us to treat an index as a variable, we can also consider the function defined by 