Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T12:59:17.596Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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