Journal of Symbolic Logic

Recursively Enumerable Generic Sets

Wolfgang Maass

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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.

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

First available in Project Euclid: 6 July 2007

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Maass, Wolfgang. Recursively Enumerable Generic Sets. J. Symbolic Logic 47 (1982), no. 4, 809--823.

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