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Algebra and Logic

, Volume 58, Issue 3, pp 214–223 | Cite as

ω-Independent Bases for Quasivarieites of Torsion-Free Groups

  • A. I. BudkinEmail author
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It is proved that there exists a set ℛ of quasivarieties of torsion-free groups which (a) have an ω-independent basis of quasi-identities in the class 𝒦0 of torsion-free groups, (b) do not have an independent basis of quasi-identities in 𝒦0, and (c) the intersection of all quasivarieties in ℛ has an independent quasi-identity basis in 𝒦0. The collection of such sets ℛ has the cardinality of the continuum.

Keywords

quasivariety quasi-identity independent basis ω-independent basis torsion-free group. 

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Altai State UniversityBarnaulRussia

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