Abstract:
It is proved that there exists a set $\mathcal{R}$ of quasivarieties
of torsion-free groups which (a) have an $\omega$-independent basis
of quasi-identities in the class $\mathcal{K}_{0}$ of torsion-free
groups, (b) do not have an independent basis of quasi-identities in
$\mathcal{K}_{0}$, and (c) the intersection of all quasivarieties in
$\mathcal{R}$ has an independent quasi-identity basis in
$\mathcal{K}_{0}$. The collection of such sets $\mathcal{R}$ has the
cardinality of the continuum.
Citation:
A. I. Budkin, “$\omega$-Independent bases for quasivarieites
of torsion-free groups”, Algebra Logika, 58:3 (2019), 320–333; Algebra and Logic, 58:3 (2019), 214–223
\Bibitem{Bud19}
\by A.~I.~Budkin
\paper $\omega$-Independent bases for quasivarieites
of torsion-free groups
\jour Algebra Logika
\yr 2019
\vol 58
\issue 3
\pages 320--333
\mathnet{http://mi.mathnet.ru/al897}
\crossref{https://doi.org/10.33048/alglog.2019.58.302}
\transl
\jour Algebra and Logic
\yr 2019
\vol 58
\issue 3
\pages 214--223
\crossref{https://doi.org/10.1007/s10469-019-09539-x}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074831445}
Linking options:
https://www.mathnet.ru/eng/al897
https://www.mathnet.ru/eng/al/v58/i3/p320
This publication is cited in the following 3 articles:
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. IV. Nonstandard quasivarieties”, Siberian Math. J., 62:5 (2021), 850–858
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
M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051
Citation in format AMSBIB
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