A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. Èlektron. Mat. Izv., 14 (2017), 252

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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. Basheyeva^a, A. Nurakunov^b, M. Schwidefsky^cd, A. Zamojska-Dzienio^e

^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

Full-text PDF (179 kB) Citations (13)

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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

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\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

Lattices of subclasses
M. V. Semenova, A. Zamojska-Dzienio
Sibirsk. Mat. Zh., 2012, 53:5, 1111–1132
Lattices of subclasses. III
A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio
Sib. Èlektron. Mat. Izv., 2017, 14, 252–263

This publication is cited in the following 13 articles:

M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513
M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785
A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783
M. V. Schwidefsky, “On a class of subsemigroup lattices”, Siberian Math. J., 61:5 (2020), 941–952
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
M. V. Schwidefsky, “on Sufficient Conditions For Q-Universality”, Sib. Electron. Math. Rep., 17 (2020), 1043–1051
A. I. Budkin, “Ob $\omega $-nezavisimosti kvazimnogoobrazii nilpotentnykh grupp”, Sib. elektron. matem. izv., 16 (2019), 516–522
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. II. Undecidable problems”, Algebra and Logic, 58:2 (2019), 123–136
A. I. Budkin, “$\omega$-Independent bases for quasivarieites of torsion-free groups”, Algebra and Logic, 58:3 (2019), 214–223
M. V. Schwidefsky, “Existence of independent quasi-equational bases”, Algebra and Logic, 58:6 (2020), 514–537
A. O. Basheyeva, M. V. Schwidefsky, “Quasiequational bases of Cantor algebras”, Siberian Math. J., 59:3 (2018), 375–382
A. O. Basheeva, A. V. Yakovlev, “Ob $\omega$-nezavisimykh bazisakh kvazitozhdestv”, Sib. elektron. matem. izv., 14 (2017), 838–847
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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