Vol. 31, No. 3, 1969

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A rate of growth criterion for universality of regressive isols

Judith Lee Gersting

Vol. 31 (1969), No. 3, 669–677

Let α be an infinite retraceable set having the property that if an is the retraceable function ranging over α, then for each partial recursive function p(x), there is a number m such that p(an) < an+1 whenever n m and p(an) is defined. Recently, T. G. McLaughlin proved the existence of retraceable sets having this property and also of such sets having recursively enumerable complements. In addition, he showed that sets of this kind will be immune and that each of their regressive subsets will be retraceable. The main result of this paper states that (infinite) regressive isols that contain a retraceable set with this property will be universal. As corollary to this result we obtain the existence of cosimple universal regressive isols.

Mathematical Subject Classification
Primary: 02.72
Received: 19 June 1968
Published: 1 December 1969
Judith Lee Gersting