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This article is cited in 19 scientific papers (total in 19 papers)
Structure of Quasivariety Lattices. I. Independent Axiomatizability
A. V. Kravchenkoabcd, A. M. Nurakunove, M. V. Schwidefskyad a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Siberian Institute of Management — Branch of the Russian Presidental Academy of National Economics and Public Administration, Novosibirsk
c Novosibirsk State Technical University
d Novosibirsk State University
e Institute of Mathematics of the National Academy of Sciences of the Kyrgyz Republic
Abstract:
We find a sufficient condition for a quasivariety $\mathbf{K}$ to have continuum many subquasivarieties that have no independent quasi-equational bases relative to $\mathbf{K}$ but have $\omega$-independent quasi-equational bases relative to $\mathbf{K}$. This condition also implies that $\mathbf{K}$ is $Q$-universal.
Keywords:
independent basis, quasi-identity, quasivariety, quasivariety lattice, Q-universality.
Received: 21.06.2017 Revised: 02.07.2018
Citation:
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of Quasivariety Lattices. I. Independent Axiomatizability”, Algebra Logika, 57:6 (2018), 684–710; Algebra and Logic, 57:6 (2019), 445–462
Linking options:
https://www.mathnet.ru/eng/al874 https://www.mathnet.ru/eng/al/v57/i6/p684
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