Let f(x) be a recursive
function and let Df(X) denote the Nerode canonical extension of f to the isols.
Let A and Y be particular isols such that Df(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 Df(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.
