Vol. 43, No. 2, 1972

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On solutions in the regressive isols

Joseph Barback

Vol. 43 (1972), No. 2, 283–296

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.

Mathematical Subject Classification
Primary: 02F40
Received: 21 May 1971
Revised: 18 July 1972
Published: 1 November 1972
Joseph Barback