Abstract:
We give a sufficient condition for a quasivariety K, weaker than the one found earlier by A. V. Kravchenko, A. M. Nurakunov, and the author, which ensures that K contains continuum many subquasivarieties with no independent quasi-equational basis relative to K. This condition holds, in particular, for any almost ff-universal quasivariety K.
Citation:
M. V. Schwidefsky, “Existence of independent quasi-equational bases”, Algebra Logika, 58:6 (2019), 769–803; Algebra and Logic, 58:6 (2020), 514–537
This publication is cited in the following 6 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
M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785
M. E. Adams, W. Dziobiak, H. P. Sankappanavar, “A relatively finite-to-finite universal but not Q-universal quasivariety”, Algebra Univers., 83:3 (2022)
M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051