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Algebra and Logic

, Volume 56, Issue 4, pp 337–347 | Cite as

Universal Generalized Computable Numberings and Hyperimmunity

  • M. Kh. FaizrakhmanovEmail author
Article

Generalized computable numberings relative to hyperimmune and high oracles are studied. We give a description of oracles relative to which every finite computable family has a universal computable numbering. Also we present a characterization of the class of oracles relative to which every universal computable numbering of an arbitrary finite family is precomplete, and establish a sufficient condition for universal generalized computable numberings to be precomplete. In addition, we look into the question on limitedness of universal numberings computable relative to high oracles.

Keywords

generalized computable numbering universal numbering precomplete numbering hyperimmune set high set 

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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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