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Structure of Quasivariety Lattices. I. Independent Axiomatizability

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We find a sufficient condition for a quasivariety K to have continuum many subquasivarieties that have no independent quasi-equational bases relative to K but have ω-independent quasi-equational bases relative to K. This condition also implies that K is Q-universal.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. V. Kravchenko & M. V. Schwidefsky

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    A. V. Kravchenko & M. V. Schwidefsky

  3. Siberian Institute of Management, ul. Nizhegorodskaya 6, Novosibirsk, 630102, Russia

    A. V. Kravchenko

  4. Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630073, Russia

    A. V. Kravchenko

  5. Institute of Mathematics, National Academy of Science of the Kyrgyz Republic, pr. Chui 265a, 720071, Bishkek, Kyrgyzstan

    A. M. Nurakunov

Authors
  1. A. V. Kravchenko
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  2. A. M. Nurakunov
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  3. M. V. Schwidefsky
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Corresponding author

Correspondence to A. V. Kravchenko.

Additional information

A. V. Kravchenko and M. V. Schwidefsky supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools, grant NSh-6848.2016.1.

M. Nurakunov supported by the International Mathematical Center of Novosibirsk State University.

Translated from Algebra i Logika, Vol. 57, No. 6, pp. 684-710, November-December, 2018.

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Kravchenko, A.V., Nurakunov, A.M. & Schwidefsky, M.V. Structure of Quasivariety Lattices. I. Independent Axiomatizability. Algebra Logic 57, 445–462 (2019). https://doi.org/10.1007/s10469-019-09516-4

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  • DOI: https://doi.org/10.1007/s10469-019-09516-4

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