Geodesic
On the сomplexity of quasivariety lattices
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 92-97

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We prove that any AD-class of algebraic structures of finite signature contains continuum many proper subclasses, which have the Nurakunov non-computability property, but which are not Q-universal (among those are almost all the known Q-universal quasivarieties nowadays). A similar result holds for some classes of algebraic structures of countable signature. This provides a negative answer to an open question.
Keywords: computable set, lattice, quasivariety, Q-universality. 
@article{SEMR_2017_14_a1,
     author = {S. M. Lutsak},
     title = {On the {\cyrs}omplexity of quasivariety lattices},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {92--97},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a1/}
}
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S. M. Lutsak. On the сomplexity of quasivariety lattices. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 92-97. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a1/