COMPLEXITY OF QUASIVARIETY LATTICES

If a quasivariety A of algebraic systems of finite signature satisfies some generalization of a sufficient condition for Q-universality treated by M. E. Adams and W. A. Dziobiak, then, for any at most countable set {S-i | i is an element of I} of finite semilattices, the lattice Pi(i is an element of I) Sub(S-i) is a homomorphic image of some sublattice of a quasivariety lattice Lq(A). Specifically, there exists a subclass K subset of A such that the problem of embedding a finite lattice in a lattice Lq(K) of K-quasivarieties is undecidable. This, in particular, implies a recent result of A. M. Nurakunov.