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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, Volume 15, Issue 1, Pages 29–44 (Mi vngu360)  

Boolean algebras with distinguished endomorphisms and generating trees

N. A. Bazhenovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: We obtain a characterization of computable Boolean algebras with distinguished endomorphisms in terms of generating trees and mappings of the trees. We prove that every degree spectrum of a countable family of subsets of $\omega$ is a degree spectrum of some natural enrichment of a Boolean algebra.

Keywords: Boolean algebra, Boolean algebra with distinguished endomorphisms, degree spectrum, computable dimension.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-860.2014.1
2014/139
Russian Foundation for Basic Research 14-01-00376


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English version:
Journal of Mathematical Sciences, 2016, 215:4, 460–474

UDC: 510.5+510.6+512.563
Received: 31.07.2013

Citation: N. A. Bazhenov, “Boolean algebras with distinguished endomorphisms and generating trees”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:1 (2015), 29–44; J. Math. Sci., 215:4 (2016), 460–474

Citation in format AMSBIB
\Bibitem{Baz15}
\by N.~A.~Bazhenov
\paper Boolean algebras with distinguished endomorphisms and generating trees
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2015
\vol 15
\issue 1
\pages 29--44
\mathnet{http://mi.mathnet.ru/vngu360}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 215
\issue 4
\pages 460--474
\crossref{https://doi.org/10.1007/s10958-016-2851-9}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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