 Let \(\mathsf{T}\) be a consistent, computably axiomatizable theory extending \(\mathsf{Q}\) (i.e., Robinson arithmetic). Then the class of functions \(\mathbf{F}_{\mathsf{T}}\) which is representable in \(\mathsf{T}\) in the sense of (\ref{repfun}) above (with \(\mathsf{T}\) replacing \(\mathsf{P}\)) is such that \(\mathbf{F}_{\mathsf{T}} = \mathbf{GR}\). (See  representability in the entry on Gödel’s incompleteness theorems  and Odifreddi (1989, ch. I.3).)