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

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

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
\Bibitem{Baz13} \by N.~A.~Bazhenov \paper Computable numberings of the class of Boolean algebras with distinguished endomorphisms \jour Algebra Logika \yr 2013 \vol 52 \issue 5 \pages 535--552 \mathnet{http://mi.mathnet.ru/al601} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184658} \transl \jour Algebra and Logic \yr 2013 \vol 52 \issue 5 \pages 355--366 \crossref{https://doi.org/10.1007/s10469-013-9247-4} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000328340100001} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888993284} 

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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, “Boolean algebras with distinguished endomorphisms and generating trees”, J. Math. Sci., 215:4 (2016), 460–474
2. A. K. Voǐtov, “The $\Delta^0_\alpha$-computable enumerations of the classes of projective planes”, Siberian Math. J., 59:2 (2018), 252–263
3. Mahmoud M.A., “Degrees of Categoricity of Trees and the Isomorphism Problem”, Math. Log. Q., 65:3 (2019), 293–304
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