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.
Fulltext:
PDF file (220 kB)
