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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 13 scientific papers (total in 13 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
References:
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}
Linking options:
  • https://www.mathnet.ru/eng/semr782
  • https://www.mathnet.ru/eng/semr/v14/p252
    Cycle of papers
    This publication is cited in the following 13 articles:
    1. M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513  mathnet  crossref
    2. M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785  mathnet  crossref
    3. A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783  mathnet  crossref  mathscinet
    4. M. V. Schwidefsky, “On a class of subsemigroup lattices”, Siberian Math. J., 61:5 (2020), 941–952  mathnet  crossref  crossref  isi  elib
    5. A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. elektron. matem. izv., 17 (2020), 753–768  mathnet  crossref
    6. M. V. Schwidefsky, “on Sufficient Conditions For Q-Universality”, Sib. Electron. Math. Rep., 17 (2020), 1043–1051  mathnet  crossref  mathscinet  zmath  isi  scopus
    7. A. I. Budkin, “Ob $\omega $-nezavisimosti kvazimnogoobrazii nilpotentnykh grupp”, Sib. elektron. matem. izv., 16 (2019), 516–522  mathnet  crossref
    8. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. II. Undecidable problems”, Algebra and Logic, 58:2 (2019), 123–136  mathnet  crossref  crossref  isi
    9. A. I. Budkin, “$\omega$-Independent bases for quasivarieites of torsion-free groups”, Algebra and Logic, 58:3 (2019), 214–223  mathnet  crossref  crossref  isi
    10. M. V. Schwidefsky, “Existence of independent quasi-equational bases”, Algebra and Logic, 58:6 (2020), 514–537  mathnet  crossref  crossref  isi
    11. A. O. Basheyeva, M. V. Schwidefsky, “Quasiequational bases of Cantor algebras”, Siberian Math. J., 59:3 (2018), 375–382  mathnet  crossref  crossref  isi  elib
    12. A. O. Basheeva, A. V. Yakovlev, “Ob $\omega$-nezavisimykh bazisakh kvazitozhdestv”, Sib. elektron. matem. izv., 14 (2017), 838–847  mathnet  crossref
    13. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On quasi-equational bases for differential groupoids and unary algebras”, Sib. elektron. matem. izv., 14 (2017), 1330–1337  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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