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Algebra and Logic

, Volume 52, Issue 5, pp 355–366 | Cite as

Computable Numberings of the Class of Boolean Algebras with Distinguished Endomorphisms

  • N. A. Bazhenov
Article

We deal with computable Boolean algebras having a fixed finite number λ of distinguished endomorphisms (briefly, E λ -algebras). It is shown that the index set of E λ -algebras is \( \Pi_2^0 \)-complete. It is proved that the class of all computable E λ -algebras has a \( \Delta_3^0 \)-computable numbering but does not have a \( \Delta_2^0 \)-computable numbering up to computable isomorphism. Also for the class of all computable E λ -algebras, we explore whether there exist hyperarithmetical Friedberg numberings up to \( \Delta_{\alpha}^0 \)-computable isomorphism.

Keywords

computable Boolean algebra with distinguished endomorphisms computable numbering Friedberg numbering index set isomorphism problem 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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