Abstract
We find sufficient conditions guaranteeing that for a quasivariety [Formula: see text] of structures of finite type containing a [Formula: see text]-class with respect to [Formula: see text], there exists a subquasivariety [Formula: see text] and a structure [Formula: see text] such that the problems whether a finite lattice embeds into the lattice [Formula: see text] of [Formula: see text]-varieties and into the lattice [Formula: see text] are undecidable.
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