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Siberian Mathematical Journal

, Volume 60, Issue 3, pp 464–471 | Cite as

Partial Decidable Presentations in Hyperarithmetic

  • I. Sh. KalimullinEmail author
  • V. G. PuzarenkoEmail author
  • M. Kh. FaizrahmanovEmail author
Article

Abstract

We study the problem of the existence of decidable and positive \(\Pi_1^1\)- and \(\Sigma_1^1\)-numberings of the families of \(\Pi_1^1\)- and \(\Sigma_1^1\)-cones with respect to inclusion. Some laws are found that reflect the presence of decidable computable \(\Pi_1^1\)- and \(\Sigma_1^1\)-numberings of these families in dependence on the analytical complexity of the set defining a cone.

Keywords

numbering decidable numbering positive numbering computable numbering computable set computably enumerable set e-reducibility hyperarithmetic set constructible admissible set 

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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia
  2. 2.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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