Representability theorem for computable functions

https://arbital.com/p/representability_theorem_for_computable_functions

by Jaime Sevilla Molina Sep 21 2016


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)}$~$.