On solutions in the regressive isols

Joseph Barback
1972 Pacific Journal of Mathematics  
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
more » ... 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.
doi:10.2140/pjm.1972.43.283 fatcat:a3hw4hsgcbhg7blcv7bgnto5le