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ω-Independent Bases for Quasivarieites of Torsion-Free Groups

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Algebra and Logic Aims and scope

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.

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  1. Altai State University, pr. Lenina 61, Barnaul, 656049, Russia

    A. I. Budkin

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  1. A. I. Budkin
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Correspondence to A. I. Budkin.

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Translated from Algebra i Logika, Vol. 58, No. 3, pp. 320-333, May-June, 2019.

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Budkin, A.I. ω-Independent Bases for Quasivarieites of Torsion-Free Groups. Algebra Logic 58, 214–223 (2019). https://doi.org/10.1007/s10469-019-09539-x

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