On solutions in the regressive isols
Joseph Barback · Pacific Journal of Mathematics · 1972
Let f(x) be a recursive function and let D f (X) denote the Nerode canonical extension of /to the isols.Let A and Y be particular isols such that D f (A) = Y.The main results in the paper deal with the following problem: if one of the isols A and Y is regressive, what regressive property if any will the other isol have.It is shown that if A is a regressive isol then Y will be also.Also, it is possible for Y to be a regressive isol while A is not.In this event there exist regressive isols B with D f (B) = Y and B ^ΛA.Extensions of these results for recursive functions of more than one variable are discussed in the last section of the paper.