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Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 848–855 (Mi semr827)  

Mathematical logic, algebra and number theory

Boolean algebras realized by c.e. equivalence relations

N. Bazhenovab, M. Mustafac, F. Stephand, M. Yamaleeve

a Novosibirsk State University, 2 Pirogova St., 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug Av., 630090, Novosibirsk, Russia
c Department of Mathematics, School of Science and Technology, Nazarbayev University, 53, Kabanbay Batyr Avenue, Astana, 010000, Republic of Kazakhstan
d Department of Computer Science and Department of Mathematics, National University of Singapore, 119076, Republic of Singapore
e N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, 18 Kremlevskaya Str., Kazan, 420008, Russia

Abstract: Let $E$ be a computably enumerable (c.e.) equivalence relation on the set of natural numbers $\omega$. We consider countable structures where basic functions are computable and respect $E$. If the corresponding quotient structure is a Boolean algebra $B$, then we say that the c.e. relation $E$ realizes $B$. In this paper we study connections between algorithmic properties of $E$ and algebraic properties of Boolean algebras realized by $E$. Also we compare these connections with the corresponding results for linear orders and groups realized by c.e. equivalence relations.

Keywords: computability theory, Boolean algebras, equivalence relations, computably enumerable structures.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-60058_мол_а_дк
15-41-02507_р_поволжье_а
Ministry of Education and Science of the Russian Federation 1.1515.2017
N. Bazhenov was supported by RFBR, according to the research project No. 16-31-60058 mol_a_dk. M. Yamaleev was supported by RFBR project 15-41-02507, by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities 1.1515.2017, and by the research grant of Kazan Federal University.


DOI: https://doi.org/10.17377/semi.2017.14.071

Full text: PDF file (154 kB)
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Document Type: Article
UDC: 510.5
MSC: 03D45
Received June 29, 2017, published August 18, 2017
Language: English

Citation: N. Bazhenov, M. Mustafa, F. Stephan, M. Yamaleev, “Boolean algebras realized by c.e. equivalence relations”, Sib. Èlektron. Mat. Izv., 14 (2017), 848–855

Citation in format AMSBIB
\Bibitem{BazMusSte17}
\by N.~Bazhenov, M.~Mustafa, F.~Stephan, M.~Yamaleev
\paper Boolean algebras realized by c.e. equivalence relations
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 848--855
\mathnet{http://mi.mathnet.ru/semr827}
\crossref{https://doi.org/10.17377/semi.2017.14.071}


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