 In the case that \(f(y)\) and \(g(y)\) are primitive recursive, we have remarked that it is possible to show that there exists a unique function \(h(y)\) satisfying (\ref{recex}) by an external set-theoretic argument. But we may also consider the case in which \(g(y)\) is assumed to be computable relative to a model of computation \(\mathbf{M}\) which differs from the partial recursive functions in that it does not natively support recursion as a mode of computation—e.g., the Turing Machine model \(\mathbf{T}\) or Unlimited Register Machine model \(\mathbf{U}\). If we simply set down (\ref{recex}) as a definition in this case, we would have no a priori assurance that \(h(y)\) is computable relative to \(\mathbf{M}\) even if \(g(x)\) is.