A [ logical theory] $~$T$~$ is said to satisfy the **representability theorem for computable functions** if for every [ computable function] $~$f:\mathbb{N}\mapsto\mathbb{N}$~$ there exists a two-place formula $~$\phi_f(x,y)$~$ in the [ language] of $~$T$~$ such that for all $~$n\in \mathbb{N}$~$ we have that $~$T\vdash \forall y\ \phi_f(\textbf n,y)\leftrightarrow y=\textbf{f(n)}$~$.