 Theorem 2.3: For all \(k \in \mathbb{N}\) there exists a \(k\)+2-ary primitive recursive relation \(T_k(e,\vec{x},s)\)—the so-called Kleene \(T\)-predicate—and a primitive recursive function \(u(x)\) (not depending on \(k\)) satisfying the following condition: for all \(k\)-ary partial recursive functions \(f(\vec{x})\) there exists \(e \in \mathbb{N}\) such that for all \(\vec{n} \in \mathbb{N}^k\) 