 Theorem 3.2: For every \(k \in \mathbb{N}\), there is a \(k+1\)-ary partial computable function \(\upsilon^k\) which is universal in the sense that for all \(k\)-ary partial computable functions \(f(\vec{x})\), there is an \(i \in \mathbb{N}\) such that \(\upsilon_k(i,\vec{x}) \simeq f(\vec{x})\).