Abstract:
We prove that each quasivariety containing a B-class has continuum many subquasivarieties with finitely partitionable ω-independent quasi-equational basis.
A. V. Kravchenko and M. V. Schwidefsky are Supported by SB RAS Fundamental Research Program I.1.1, project No. 0314-2019-0003.
A. M. Nurakunov is Supported by MES RK, project No. AP05132349 “Computability, interpretability and algebraic structure.”
M. V. Schwidefsky is Supported by Russian Science Foundation, project No. 19-11-00209 (results of Sec. 9).
Citation:
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. III. Finitely partitionable bases”, Algebra Logika, 59:3 (2020), 323–333; Algebra and Logic, 59:3 (2020), 222–229
This publication is cited in the following 10 articles:
M. V. Schwidefsky, “Existence of Independent Quasi-Equational Bases. II”, Algebra Logic, 2024
M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513
Anvar M. Nurakunov, Marina V. Schwidefsky, “Profinite Locally Finite Quasivarieties”, Stud Logica, 2023
A. I. Budkin, “On the independent axiomatizability of quasivarieties of nilpotent groups”, Siberian Math. J., 64:1 (2023), 22–32
M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785
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
Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida, CMS/CAIMS Books in Mathematics, 3, A Primer of Subquasivariety Lattices, 2022, 1
A. I. Budkin, “Independent axiomatizability of quasivarieties of torsion-free nilpotent groups”, Algebra and Logic, 60:2 (2021), 79–88
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. IV. Nonstandard quasivarieties”, Siberian Math. J., 62:5 (2021), 850–858