Geodesic
Structure of quasivariety lattices. III. Finitely partitionable bases
Algebra i logika, Tome 59 (2020) no. 3, pp. 323-333.

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We prove that each quasivariety containing a $\mathrm{B}$-class has continuum many subquasivarieties with finitely partitionable $\omega$-independent quasi-equational basis.
Keywords: independent basis, quasi-identity, quasivariety, finitely partitionable basis. 
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     title = {Structure of quasivariety lattices. {III.} {Finitely} partitionable bases},
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A. V. Kravchenko; A. M. Nurakunov; M. V. Schwidefsky. Structure of quasivariety lattices. III. Finitely partitionable bases. Algebra i logika, Tome 59 (2020) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/AL_2020_59_3_a3/

[1] A. V. Kravchenko, A. M. Nurakunov, M. V. Shvidefski, “O stroenii reshetok kvazimnogoobrazii. I. Nezavisimaya aksiomatiziruemost”, Algebra i logika, 57:6 (2018), 684–710 | MR

[2] A. V. Kravchenko, A. M. Nurakunov, M. V. Shvidefski, “O stroenii reshetok kvazimnogoobrazii. II. Nerazreshimye problemy”, Algebra i logika, 58:2 (2019), 179–199 | Zbl

[3] A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On representation of finite lattices”, Algebra Univers, 80:1 (2019), 15, 17 pp. | DOI | MR | Zbl

[4] A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On the complexity of the lattices of varieties and congruences”, Internat. J. Algebra Comput., 2020 (to appear) | DOI | MR

[5] V. K. Kartashov, “Kvazimnogoobraziya unarov s konechnym chislom tsiklov”, Algebra i logika, 19:2 (1980), 173–193 | MR

[6] A. O. Basheeva, A. V. Yakovlev, “Ob $\omega$-nezavisimykh bazisakh kvazitozhdestv”, Sib. elektron. matem. izv., 14 (2017), 838–847 http://semr.math.nsc.ru/v14/p838-847.pdf | MR

[7] A. O. Basheeva, M. V. Shvidefski, “Bazisy kvazitozhdestv kantorovykh algebr”, Sib. matem. zh., 59:3 (2018), 481–490 | MR | Zbl

[8] A. I. Budkin, “Ob $\omega$-nezavisimosti kvazimnogoobrazii nilpotentnykh grupp”, Sib. elektron. matem. izv., 16 (2019), 516–522 http://semr.math.nsc.ru/v16/p516-522.pdf | Zbl

[9] A. I. Budkin, “Ob $\omega$-nezavisimykh bazisakh kvazimnogoobrazii grupp bez krucheniya”, Algebra i logika, 58:3 (2019), 320–333 | Zbl

[10] V. A. Gorbunov, Algebraicheskaya teoriya kvazimnogoobrazii, Sibirskaya shkola algebry i logiki, Nauch. kniga, Novosibirsk, 1999

[11] A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On quasi-equational bases for differential groupoids and unary algebras”, Sib. elektron. matem. izv., 14 (2017), 1330–1337 http://semr.math.nsc.ru/v14/p1330-1337.pdf | MR | Zbl

[12] A. V. Kravchenko, “On the lattices of quasivarieties of differential groupoids”, Commentat. Math. Univ. Carol., 49:1 (2008), 11–17 | MR | Zbl

[13] A. V. Kravchenko, “O slozhnosti reshetok kvazimnogoobrazii dlya mnogoobrazii unarnykh algebr. II”, Sib. elektron. matem. izv., 13 (2016), 388–394 http://semr.math.nsc.ru/v13/p388-394.pdf | Zbl

[14] A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. elektron. matem. izv., 17 (2020), 753–768 http://semr.math.nsc.ru/v17/p753-768.pdf | MR | Zbl