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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A. Kravchenko

Sobolev Institute of Mathematics; Novosibirsk State University; Siberian Institute of Management; Novosibirsk State Technical University

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Email: a.v.kravchenko@mail.ru
俄罗斯联邦, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090; ul. Nizhegorodskaya 6, Novosibirsk, 630102; pr. Marksa 20, Novosibirsk, 630073

A. Nurakunov

Institute of Mathematics, National Academy of Science of the Kyrgyz Republic

Email: a.v.kravchenko@mail.ru
吉尔吉斯斯坦, pr. Chui 265a, Bishkek, 720071

M. Schwidefsky

Sobolev Institute of Mathematics; Novosibirsk State University

Email: a.v.kravchenko@mail.ru
俄罗斯联邦, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090

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