Abstract:
We find a sufficient condition for a quasivariety KK to have continuum many subquasivarieties that have no independent quasi-equational bases relative to KK but have ωω-independent quasi-equational bases relative to KK. This condition also implies that KK is QQ-universal.
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
This publication is cited in the following 21 articles:
M. V. Schwidefsky, “Existence of Independent Quasi-Equational Bases. II”, Algebra Logic, 2024
A. I. Budkin, “On the independent axiomatizability of quasivarieties of nilpotent groups”, Siberian Math. J., 64:1 (2023), 22–32
M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513
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A. V. Kravchenko, “On directed and finitely partitionable bases for quasi-identities”, Sib. elektron. matem. izv., 19:2 (2022), 741–746
A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783
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A. I. Budkin, “Independent axiomatizability of quasivarieties of torsion-free nilpotent groups”, Algebra and Logic, 60:2 (2021), 79–88
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M. V. Schwidefsky, “On a class of subsemigroup lattices”, Siberian Math. J., 61:5 (2020), 941–952
A. I. Budkin, “On the quasivarieties generated by a finite group and lacking any independent bases of quasi-identities”, Siberian Math. J., 61:6 (2020), 983–993
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. III. Finitely partitionable bases”, Algebra and Logic, 59:3 (2020), 222–229
A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. elektron. matem. izv., 17 (2020), 753–768
M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On the Complexity of the Lattices of Subvarieties and Congruences”, Int. J. Algebr. Comput., 30:8 (2020), 1609–1624
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. II. Undecidable problems”, Algebra and Logic, 58:2 (2019), 123–136
M. V. Schwidefsky, “Existence of independent quasi-equational bases”, Algebra and Logic, 58:6 (2020), 514–537