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Computable Homogeneous Boolean Algebras and a Metatheorem

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics SB RAS, Akademika Koptyuga Prospekt, 4, Novosibirsk, 630090, Russia

    P. E. Alaev

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  1. P. E. Alaev
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Alaev, P.E. Computable Homogeneous Boolean Algebras and a Metatheorem. Algebra and Logic 43, 73–87 (2004). https://doi.org/10.1023/B:ALLO.0000020844.03135.a6

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  • DOI: https://doi.org/10.1023/B:ALLO.0000020844.03135.a6

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