Algebra and Logic

, Volume 43, Issue 2, pp 73–87

Computable Homogeneous Boolean Algebras and a Metatheorem

  • P. E. Alaev

DOI: 10.1023/B:ALLO.0000020844.03135.a6

Cite this article as:
Alaev, P.E. Algebra and Logic (2004) 43: 73. doi:10.1023/B:ALLO.0000020844.03135.a6


We consider computable homogeneous Boolean algebras. Previously, countable homogeneous Boolean algebras have been described up to isomorphism and a simple criterion has been found for the existence of a strongly constructive (decidable) isomorphic copy for such. We propose a natural criterion for the existence of a constructive (computable) isomorphic copy. For this, a new hierarchy of \({\emptyset ^{(\omega )}} \)-computable functions and sets is introduced, which is more delicate than Feiner's. Also, a metatheorem is proved connecting computable Boolean algebras and their hyperarithmetical quotient algebras.

computable homogeneous Boolean algebra constructive copy for an algebra hierarchy 

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • P. E. Alaev
    • 1
  1. 1.Institute of Mathematics SB RASNovosibirskRussia

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