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1-reducibility inside an m-degree with a maximal set

Published online by Cambridge University Press:  12 March 2014

E. Herrmann
E. Herrmann*
Affiliation:
Fach Bereich Mathematik, Humboldt-Universität, O-1086 Berlin, Germany
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Abstract

The structure of the 1-degrees included in an m-degree with a maximal set together with the 1-reducibility relation is characterized. For this a special sublattice of the lattice of recursively enumerable sets under the set-inclusion is used.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 3 , September 1992 , pp. 1046 - 1056
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

[He83]Herrmann, E., Definable Boolean pairs in the lattice of recursively enumerable sets, Proceedings of the first Easter conference on model theory (Diederichshagen, 1983), Seminarberichte, no. 49, Sektion Mathematik, Humboldt-Universität, Berlin, pp. 42–67.Google Scholar
[He85]Herrmann, E., Maximal sets (a survey on the maximal sets inside the theory of recursively enumerable sets and their degrees) (typewritten manuscript).Google Scholar
[He86]Herrmann, E., Automorphisms of the lattice of recursively enumerable sets and hyperhypersimple sets, Proceedings of the fourth Easter conference on model theory (Grošz Köris, 1986), Seminarberichte, no. 86, Sektion Mathematik, Humboldt-Universität, Berlin, pp. 69–108.Google Scholar
[La69]Lachlan, A. H., Initial segments of one-one degrees, Pacific Journal of Mathematics, vol. 29, pp. 351–366.CrossRefGoogle Scholar
[Le70]Lerman, M., Turing degrees and many-one degrees of maximal sets, this Journal, vol. 35, pp. 29–40.Google Scholar
[Od81]Odifreddi, P., Strong reducibilities, Bulletin (New Series) of the American Mathematical Society, vol. 4, pp. 37–86.CrossRefGoogle Scholar
[S087]Soare, R. I., Recursively enumerable sets and degrees (a study of computable functions and computably generated sets), Springer-Verlag, Berlin.Google Scholar