Recursively enumerable generic sets

Journal of Symbolic Logic 47 (4):809-823 (1982)
Abstract
We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions
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