Journal of Symbolic Logic

Recursively Enumerable Generic Sets

Wolfgang Maass

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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 $\mathscr{E}$ 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.

Article information

Source
J. Symbolic Logic, Volume 47, Issue 4 (1982), 809-823.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183741140

Mathematical Reviews number (MathSciNet)
MR683156

Zentralblatt MATH identifier
0498.03026

JSTOR
links.jstor.org

Citation

Maass, Wolfgang. Recursively Enumerable Generic Sets. J. Symbolic Logic 47 (1982), no. 4, 809--823. https://projecteuclid.org/euclid.jsl/1183741140


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