Two notes on recursively enumerable sets
J. C. E. Dekker · Proceedings of the American Mathematical Society · 1953
Introduction. These notes are based on E. L. Post's paper Recursively enumerable sets of positive integers and their decision problems' to which we shall refer as RES. The reader is assumed to be familiar with ??1-5 and 9 of this paper. In the first note we shall discuss some algebraic properties of simple and hypersimple sets. In the second note we shall prove the existence of a recursively enumerable set which is neither recursive nor creative nor simple and discuss its degree of unsolvability relative to one-one reducibility and relative to many-one reducibility.