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

  • E. Herrmann (a1)

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.

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References

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[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. 4267.
[He85]Herrmann, E., Maximal sets (a survey on the maximal sets inside the theory of recursively enumerable sets and their degrees) (typewritten manuscript).
[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. 69108.
[La69]Lachlan, A. H., Initial segments of one-one degrees, Pacific Journal of Mathematics, vol. 29, pp. 351366.
[Le70]Lerman, M., Turing degrees and many-one degrees of maximal sets, this Journal, vol. 35, pp. 2940.
[Od81]Odifreddi, P., Strong reducibilities, Bulletin (New Series) of the American Mathematical Society, vol. 4, pp. 3786.
[S087]Soare, R. I., Recursively enumerable sets and degrees (a study of computable functions and computably generated sets), Springer-Verlag, Berlin.

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