Geodesic
Existence of independent quasi-equational bases. II
Algebra i logika, Tome 62 (2023) no. 6, pp. 762-785.

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

If a certain condition holds for a quasivariety $\mathbf{K}$ then $\mathbf{K}$ contains continuum many subquasivarieties having a finitely partitionable $\omega$-independent quasi-equational basis relative to $\mathbf{K}$. This is true, in particular, for each almost $ff$-universal quasivariety $\mathbf{K}$.
Keywords: quasivariety, independent quasi-equational basis, $ff$-universal quasivariety. 
@article{AL_2023_62_6_a3,
     author = {M. V. Schwidefsky},
     title = {Existence of independent quasi-equational bases. {II}},
     journal = {Algebra i logika},
     pages = {762--785},
     publisher = {mathdoc},
     volume = {62},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_6_a3/}
}
TY  - JOUR
AU  - M. V. Schwidefsky
TI  - Existence of independent quasi-equational bases. II
JO  - Algebra i logika
PY  - 2023
SP  - 762
EP  - 785
VL  - 62
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2023_62_6_a3/
LA  - ru
ID  - AL_2023_62_6_a3
ER  - 
%0 Journal Article
%A M. V. Schwidefsky
%T Existence of independent quasi-equational bases. II
%J Algebra i logika
%D 2023
%P 762-785
%V 62
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2023_62_6_a3/
%G ru
%F AL_2023_62_6_a3
M. V. Schwidefsky. Existence of independent quasi-equational bases. II. Algebra i logika, Tome 62 (2023) no. 6, pp. 762-785. http://geodesic.mathdoc.fr/item/AL_2023_62_6_a3/

[1] M. E. Adams, W. Dziobiak, “${\mathcal Q}$-universal quasivarieties of algebras”, Proc. Am. Math. Soc., 120:4 (1994), 1053–1059 | MR | Zbl

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

[3] M. V. Shvidefski, “O slozhnosti reshetok kvazimnogoobrazii”, Algebra i logika, 54:3 (2015), 381–398 | MR

[4] M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051 http://semr.math.nsc.ru/v17/p1043-1051.pdf | MR | Zbl

[5] 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

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

[7] A. V. Kravchenko, A. M. Nurakunov, M. V. Shvidefski, “O stroenii reshetok kvazimnogoobrazii. III. Konechno razbivaemye bazisy”, Algebra i logika, 59:3 (2020), 323–333 | MR | Zbl

[8] A. V. Kravchenko, A. M. Nurakunov, M. V. Shvidefski, “O stroenii reshetok kvazimnogoobrazii. IV. Nestandartnye kvazimnogoobraziya”, Sib. matem. zh., 62:5 (2021), 1049–1060 | Zbl

[9] M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv”, Algebra i logika, 58:6 (2019), 769–803 | MR

[10] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[11] V. Koubek, J. Sichler, “Universality of small lattice varieties”, Proc. Am. Math. Soc., 91:1 (1984), 19–24 | DOI | MR | Zbl

[12] V. Koubek, J. Sichler, “On almost universal varieties of modular lattices”, Algebra Univers., 45:2/3 (2001), 191–210 | MR | Zbl

[13] V. Koubek, J. Sichler, “Almost ${f}{f}$-universal and $Q$-universal varieties of modular $0$-lattices”, Colloq. Math., 101:2 (2004), 161–182 | DOI | MR | Zbl

[14] V. Koubek, J. Sichler, “Finitely generated almost universal varieties of $0$-lattices”, Commentat. Math. Univ. Carol., 46:2 (2005), 301–325 | MR | Zbl

[15] V. Koubek, J. Sichler, “On synchronized relatively full embeddings and $Q$-universality”, Cah. Topol. Géom. Différ. Catég., 49:4 (2008), 289–306 | MR | Zbl

[16] V. Koubek, J. Sichler, “Almost $ff$-universality implies $Q$-universality”, Appl. Categor. Struct., 17:5 (2009), 419–434 | DOI | MR | Zbl

[17] M. Demlová, V. Koubek, “Weak $\mathrm{alg}$-universality and $Q$-universality of semigroup quasivarieties”, Commentat. Math. Univ. Carol., 46:2 (2005), 257–279 | MR | Zbl

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

[19] W. Dziobiak, “On lattice identities satisfied in subquasivariety lattices of varieties of modular lattices”, Algebra Univers., 22:2/3 (1986), 205–214 | DOI | MR | Zbl

[20] A. Pultr, V. Trnková, Combinatorial, algebraic and topological representations of groups, Semigroups and categories, North-Holland Math. Lib., 22, North-Holland Publ. Co., Amsterdam–New York–Oxford, 1980 | MR | Zbl

[21] 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

[22] A. B. Romanowska, J. D. H. Smith, Modes, World Scientific, Singapore, 2002 | MR | Zbl

[23] A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of variety lattices of 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

[24] A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783 http://semr.math.nsc.ru/v19/n2/p768-783.pdf | MR | Zbl

[25] A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subklasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263 http://semr.math.nsc.ru/v14/p252-263.pdf | MR | Zbl