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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 252–263
DOI: https://doi.org/10.17377/semi.2017.14.023 (Mi semr782) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Mathematical logic, algebra and number theory

Lattices of subclasses. III

A. Basheyevaa, A. Nurakunovb, M. Schwidefskycd, A. Zamojska-Dzienioe

a The L.N. Gumilyov Eurasian National University, Satpaev str. 2, 010000 Astana, Kazakhstan
b Institute of Mathematics of the National Academy of Sciences, Chui prosp. 265a, 720071 Bishkek, Kyrgyzstan
c Sobolev Institute of Mathematics of the Siberian Branch RAS, Acad. Koptyug prosp. 4, 630090 Novosibirsk, Russia
d Novosibirsk State University, Pirogova str. 1, 630090 Novosibirsk, Russia
e Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa str. 75, 00-662 Warsaw, Poland
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DOI: https://doi.org/10.17377/semi.2017.14.023
Abstract: We prove that for certain $Q$-universal quasivarieties $\mathbf{K}$, the lattice of $\mathbf{K}$-quasivarieties contains continuum many subquasivarieties with the undecidable quasi-equational theory and for which the finite membership problem is also undecidable. Moreover, we prove that certain $Q$-universal quasivarieties have continuum many subquasivarieties with no independent quasi-equational basis.
Keywords: Abelian group, differential groupoid, finite membership problem, graph, independent basis, quasi-identity, quasi-equational theory, quasivariety, $Q$-universal, undecidable theory.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 3953/GF4
Ministry of Education and Science of the Russian Federation NSh-6848.2016.1
Warsaw University of Technology 504P/1120/0025/000
The second author was supported by the Ministry of Education and Sciences of Kazakhstan (grant 3953/GF4). The third author was supported by the Presidential Grant Council of Russian Federation (grant NSh-6848.2016.1). The fourth author was supported by the Warsaw University of Technology under statutory (grant 504P/1120/0025/000).
Received February 17, 2017, published March 24, 2017
Bibliographic databases:
Document Type: Article
UDC: 512.56, 512.57
MSC: 06B15, 08C15
Language: English
Citation: A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. Èlektron. Mat. Izv., 14 (2017), 252–263
Citation in format AMSBIB
\Bibitem{BasNurSch17}
\by A.~Basheyeva, A.~Nurakunov, M.~Schwidefsky, A.~Zamojska-Dzienio
\paper Lattices of subclasses.~III
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 252--263
\mathnet{http://mi.mathnet.ru/semr782}
\crossref{https://doi.org/10.17377/semi.2017.14.023}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000407792200027}
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  • https://www.mathnet.ru/eng/semr/v14/p252
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