Kleenes_Normal_Form_Theorem

For each integer $k \ge 1$, there exists * a primitive recursive $k+1$-ary relation $T_k$; * a primitive recursive function $U: \N \to \N$ such that a partial function $f: \N^k \to \N$ is recursive iff, for some $e \in \N$ and all $\left({n_1, n_2, \ldots, n_k}\right) \in \N^k$ $f \left({n_1, n_2, \ldots, n_k}\right) \approx U \left({\mu z \ T_k \left({e, n_1, n_2, \ldots, n_k, z}\right)}\right)$