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Siberian Mathematical Journal

, Volume 58, Issue 6, pp 1104–1110 | Cite as

The Rogers Semilattices of Generalized Computable Enumerations

  • M. Kh. Faizrahmanov
Article
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Abstract

We study the cardinality and structural properties of the Rogers semilattice of generalized computable enumerations with arbitrary noncomputable oracles and oracles of hyperimmune Turing degree. We show the infinity of the Rogers semilattice of generalized computable enumerations of an arbitrary nontrivial family with a noncomputable oracle. In the case of oracles of hyperimmune degree we prove that the Rogers semilattice of an arbitrary infinite family includes an ideal without minimal elements and establish that the top, if present, is a limit element under the condition that the family contains the inclusion-least set.

Keywords

computable enumeration generalized computable enumeration Rogers semilattice hyperimmune set minimal enumeration universal enumeration 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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