Assume $ f\colon ω × ω → ω$ is a computable function. How can we prove that there is a primitive recursive function $ g\colon ω × ω → ω$ where the following holds:
$ ∀n [∃s(f(n, s) = 1) ↔ ∃k(g(n, k) = 1)]$
So for every $ n$ , there is an $ s$ such that $ f(n, s) = 1$ if and only if there is a $ k$ such that $ g(n, k) = 1$ .
Been working on this problem for a while now, if anyone could please help?