Double Recursive Functions and Their Hierarchy

Abstract:

      This paper discusses the properties of double recursive functions which are defined by R.Peter in [3]. An equivalent characterization of double recursive functions is suggested, which is defined to be the class z = ∪_n∈w z_n of z-hierarchy. Then, a Grzegorczyk type hier-archy of double recursive functions is obtained by means of the results of [6]. Furthermore, the standard double recursion of R.Peter is reduced to a more simple scheme.