Abstract
We combine a refinement of a recent theorem of A. N. Degtev with a result of our own, in order to derive a general theorem about regressive sets which has the following Corollary. If A A is any point-decomposable π 1 0 \pi _1^0 set then A A has an infinite π 1 0 \pi _1^0 subset B B such that B B has “highly” dense-simple complement and, moreover, all infinite π 1 0 \pi _1^0 subsets of B B are effectively decomposable in a strong sense (namely, they are all retraceable).
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