Celebratio Mathematica — Appel — Complete Bibliography

Complete Bibliography

Works connected to Thomas Graham McLaughlin

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K. I. Appel and T. G. McLaughlin: “On properties of regressive sets,” Trans. Am. Math. Soc. 115 (1965), pp. 83–93. MR 230616 Zbl 0192.05202 article

It was recently demonstrated by R. Mansfield (unpublished) that complementary retraceable sets must be recursive. Our main result, proved in §3, is that at least one member of any complementary pair of regresssive sets is recursively enumerable. This is a generalization of Mansfield’s theorem, but the method of proof, in §3, is quite different. In §4, one of the two principal lemmas used by Mansfield is generalized, and some related material is developed, including an alternative derivation of the main theorem. In §5, we show that if the intersection of a pair of regressive sets is infinite then it has an infinite regressive subset. As a corollary to this last result, we prove that a coregressive hypersimple set is many-one incomparable with any hyperhypersimple set.