Impossibility of finite generation of partial recursive functions by a unary isotone operation (Q1101443)

Let A denote the set of unary partial recursive functions. It is known that there exist two elements of A which generate, via composition, all of A, and that one element will not suffice. This paper exhibits an effective binary operation on A such that a single element suffices to generate A via that operation. On the other hand, this paper also shows that for any effective unary operation on A, no finite subset of a can suffice as a generating set.