Geodesic
Complexity of quasivariety lattices
Algebra i logika, Tome 54 (2015) no. 3, pp. 381-398.

Voir la notice de l'article provenant de la source Math-Net.Ru

If a quasivariety $\mathbf A$ 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 $\{\mathcal S_i\mid i\in I\}$ of finite semilattices, the lattice $\prod_{i\in I}\operatorname{Sub}(\mathcal S_i)$ is a homomorphic image of some sublattice of a quasivariety lattice $\operatorname{Lq}(\mathbf A)$. Specifically, there exists a subclass $\mathbf{K\subseteq A}$ such that the problem of embedding a finite lattice in a lattice $\operatorname{Lq}(\mathbf K)$ of $\mathbf K$-quasivarieties is undecidable. This, in particular, implies a recent result of A. M. Nurakunov.
Keywords: computable set, lattice, quasivariety, $Q$-universality, undecidable problem, universal class, variety. 
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M. V. Schwidefsky. Complexity of quasivariety lattices. Algebra i logika, Tome 54 (2015) no. 3, pp. 381-398. http://geodesic.mathdoc.fr/item/AL_2015_54_3_a4/

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