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Algebra Logika, 2013, Volume 52, Number 5, Pages 535–552 (Mi al601)  

This article is cited in 1 scientific paper (total in 1 paper)

Computable numberings of the class of Boolean algebras with distinguished endomorphisms

N. A. Bazhenovab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We deal with computable Boolean algebras having a fixed finite number $\lambda$ of distinguished endomorphisms (briefly, $E_\lambda$-algebras). It is shown that the index set of $E_\lambda$-algebras is $\Pi^0_\2$-complete. It is proved that the class of all computable $E_\lambda$-algebras has a $\Delta^0_3$-computable numbering but does not have a $\Delta^0_2$-computable numbering, up to computable isomorphism. Also for the class of all computable $E_\lambda$-algebras, we explore whether there exist hyperarithmetical Friedberg numberings, up to $\Delta^0_\alpha$-computable isomorphism.

Keywords: computable Boolean algebra with distinguished endomorphisms, computable numbering, Friedberg numbering, index set, isomorphism problem.

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English version:
Algebra and Logic, 2013, 52:5, 355–366

Bibliographic databases:

UDC: 512.563+510.5+510.6
Received: 17.07.2013

Citation: N. A. Bazhenov, “Computable numberings of the class of Boolean algebras with distinguished endomorphisms”, Algebra Logika, 52:5 (2013), 535–552; Algebra and Logic, 52:5 (2013), 355–366

Citation in format AMSBIB
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\issue 5
\pages 535--552
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\pages 355--366
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Bazhenov, “Bulevy algebry s vydelennymi endomorfizmami i porozhdayuschie derevya”, Vestn. NGU. Ser. matem., mekh., inform., 15:1 (2015), 29–44  mathnet; N. A. Bazhenov, “Boolean algebras with distinguished endomorphisms and generating trees”, J. Math. Sci., 215:4 (2016), 460–474  crossref
  • Алгебра и логика Algebra and Logic
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