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.
