Plain Bases for Classes of Primitive Recursive Functions
Stefano Mazzanti · Mathematical logic quarterly · 2002
Abasisforaset C of functions on natural numbers is a set F of functions such that C is the closure with respect to substitution of the projection functions and the functions in F. This paper introduces three new bases, comprehending only common functions, for the Grzegorczyk classes ℰn with n ≥ 3. Such results are then applied in order to show that ℰn+1 = Kn for n ≥ 2, where {Kn}n∈ℕ is the Axt hierarchy.