Note on degrees of partial functions
John R. Myhill · Proceedings of the American Mathematical Society · 1961
The notion of one function's being recursive in another is normally considered only for full functions; but Davis [1, p. 171] has given a definition applicable also to partial functions. For one-argument functions (to which we restrict ourselves for the sake of simplicity) this reads: f is partial recursive in g if there is a completely computable functional2 I) for which f(x) =4)(g, x). And here 4) is called completely computable if for some partial recursive h we have