Covers in the lattice of varieties of ℓ-groups

Abstract

We show that a variety ν in the lattice L of varieties of l-groups has continuum many covers, and that the same is also true of an arbitrary o-approximable variety Χ with the property ν⊆Χ. It is proved that any o-approximable quasivariety Q of l-groups, for which ν⊆Q, has the continuum of covers in the quasivariety lattice Λ.