## Journal of Symbolic Logic

### Recursively Enumerable Generic Sets

Wolfgang Maass

#### 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

https://projecteuclid.org/euclid.jsl/1183741140

Mathematical Reviews number (MathSciNet)
MR683156

Zentralblatt MATH identifier
0498.03026

JSTOR