Recursively enumerable generic sets

Journal of Symbolic Logic 47 (4):809-823 (1982)
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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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Citations of this work

Splitting Theorems in Recursion Theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
Some Orbits for E.Peter Cholak, Rod Downey & Eberhard Herrmann - 2001 - Annals of Pure and Applied Logic 107 (1-3):193-226.
Definable Properties of the Computably Enumerable Sets.Leo Harrington & Robert I. Soare - 1998 - Annals of Pure and Applied Logic 94 (1-3):97-125.

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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.

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