This article is cited in 21 papers

Structure of Quasivariety Lattices. I. Independent Axiomatizability

A. V. Kravchenko^abcd, A. M. Nurakunov^e, M. V. Schwidefsky<sup>ad

a</sup> 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.

UDC: 512.57

Received: 21.06.2017
Revised: 02.07.2018

DOI: 10.33048/alglog.2018.57.604

 English version: Algebra and Logic, 2019, 57:6, 445–462

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