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Recursively enumerable generic sets

Published online by Cambridge University Press:  12 March 2014

Wolfgang Maass
Wolfgang Maass*
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 4 , December 1982 , pp. 809 - 823
Copyright
Copyright © Association for Symbolic Logic 1982

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References

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