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Algebra Logika, 2015, Volume 54, Number 3, Pages 381–398 (Mi al699)  

This article is cited in 8 scientific papers (total in 8 papers)

Complexity of quasivariety lattices

M. V. Schwidefskyab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: If a quasivariety $\mathbf A$ of algebraic systems of finite signature satisfies some generalization of a sufficient condition for $Q$-universality treated by M. E. Adams and W. A. Dziobiak, then, for any at most countable set $\{\mathcal S_i\mid i\in I\}$ of finite semilattices, the lattice $\prod_{i\in I}\operatorname{Sub}(\mathcal S_i)$ is a homomorphic image of some sublattice of a quasivariety lattice $\operatorname{Lq}(\mathbf A)$. Specifically, there exists a subclass $\mathbf{K\subseteq A}$ such that the problem of embedding a finite lattice in a lattice $\operatorname{Lq}(\mathbf K)$ of $\mathbf K$-quasivarieties is undecidable. This, in particular, implies a recent result of A. M. Nurakunov.

Keywords: computable set, lattice, quasivariety, $Q$-universality, undecidable problem, universal class, variety.

DOI: https://doi.org/10.17377/alglog.2015.54.305

Full text: PDF file (211 kB)
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English version:
Algebra and Logic, 2015, 54:3, 245–257

Bibliographic databases:

UDC: 512.56+512.57+510.53
Received: 17.09.2014
Revised: 03.05.2015

Citation: M. V. Schwidefsky, “Complexity of quasivariety lattices”, Algebra Logika, 54:3 (2015), 381–398; Algebra and Logic, 54:3 (2015), 245–257

Citation in format AMSBIB
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\by M.~V.~Schwidefsky
\paper Complexity of quasivariety lattices
\jour Algebra Logika
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\issue 3
\pages 381--398
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\crossref{https://doi.org/10.17377/alglog.2015.54.305}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3467193}
\transl
\jour Algebra and Logic
\yr 2015
\vol 54
\issue 3
\pages 245--257
\crossref{https://doi.org/10.1007/s10469-015-9344-7}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Kravchenko, “O slozhnosti reshetok kvazimnogoobrazii dlya mnogoobrazii unarnykh algebr. II”, Sib. elektron. matem. izv., 13 (2016), 388–394  mathnet  crossref
    2. S. M. Lutsak, “O slozhnosti reshetok kvazimnogoobrazii”, Sib. elektron. matem. izv., 14 (2017), 92–97  mathnet  crossref
    3. A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263  mathnet  crossref
    4. A. V. Kravchenko, A. V. Yakovlev, “Quasivarieties of graphs and independent axiomatizability”, Siberian Adv. Math., 28:1 (2018), 53–59  mathnet  crossref  crossref  elib
    5. 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
    6. S. M. Lutsak, “The complexity of quasivariety lattices of unary algebras”, Bull. Karaganda Univ-Math., 85:1 (2017), 65–70  isi
    7. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of Quasivariety Lattices. I. Independent Axiomatizability”, Algebra and Logic, 57:6 (2019), 445–462  mathnet  crossref  crossref  isi
    8. A. V. Kravchenko, A. M. Nurakunov, M. V. Shvidefski, “O stroenii reshetok kvazimnogoobrazii. II. Nerazreshimye problemy”, Algebra i logika, 58:2 (2019), 179–199  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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