Abstract

Let ℸ be the set of Gödel numbers Gn of function symbols f such that PRA ⊢ and let γ be the function such that equation imageWe prove: The r. e. set ℸ is m-complete; the function γ is not primitive recursive in any class of functions {f1, f2, ⃛} so long as each fi has a recursive upper bound. This implies that γ is not primitive recursive in ℸ although it is recursive in ℸ