Two Notes on Recursive Functions

Introduction. The theory of regressive isols was introduced by J. C. E. Dekker in [7]. The results that we wish to present in this paper belong to this theory and is a continuation of some of our studies in [1], [3] and [4]. We will assume that the reader is familiar with the terminology and some of the main results of the papers listed as references. We let E denote the collection of all nonnegative integers (numbers), A the collection of all isols, A* the collection of all isolic integers, and AB the collection of all regressive isols. If/is a function from a subset of E into E then 8/ will denote its domain and pf its range. Let un and vn be two one-to-one functions from E into E. Then un ̂ * vn, if there is a partial recursive function / such that