Geodesic
Structure of quasivariety lattices. II. Undecidable problems
Algebra i logika, Tome 58 (2019) no. 2, pp. 179-199

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Sufficient conditions are specified under which a quasivariety contains continuum many subquasivarieties having an independent quasi-equational basis but for which the quasi-equational theory and the finite membership problem are undecidable. A number of applications are presented.
Keywords: quasi-identity, quasivariety, membership problem, undecidable theory, $Q$-universality, independent basis. 
@article{AL_2019_58_2_a2,
     author = {A. V. Kravchenko and A. M. Nurakunov and M. V. Schwidefsky},
     title = {Structure of quasivariety lattices. {II.} {Undecidable} problems},
     journal = {Algebra i logika},
     pages = {179--199},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_2_a2/}
}
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A. V. Kravchenko; A. M. Nurakunov; M. V. Schwidefsky. Structure of quasivariety lattices. II. Undecidable problems. Algebra i logika, Tome 58 (2019) no. 2, pp. 179-199. http://geodesic.mathdoc.fr/item/AL_2019_58_2_a2/