Geodesic
$\omega$-Independent bases for quasivarieites
Algebra i logika, Tome 58 (2019) no. 3, pp. 320-333

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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.
Keywords: quasivariety, quasi-identity, independent basis, $\omega$-independent basis
Mots-clés : torsion-free group. 
@article{AL_2019_58_3_a1,
     author = {A. I. Budkin},
     title = {$\omega${-Independent} bases for quasivarieites},
     journal = {Algebra i logika},
     pages = {320--333},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_3_a1/}
}
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A. I. Budkin. $\omega$-Independent bases for quasivarieites. Algebra i logika, Tome 58 (2019) no. 3, pp. 320-333. http://geodesic.mathdoc.fr/item/AL_2019_58_3_a1/