Geodesic
On directed and finitely partitionable bases for quasi-identities
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 741-746.

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

We prove that, under certain conditions on a quasivariety, there exists continuum many subquasivarieties of this quasivariety with both finitely partitionable (independent) and directed bases for quasi-identities. We also notice that such a situation is impossible for bases for anti-identities.
Keywords: quasivariety, basis for quasi-identities. 
@article{SEMR_2022_19_2_a3,
     author = {A. V. Kravchenko},
     title = {On directed and finitely partitionable bases for quasi-identities},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {741--746},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a3/}
}
TY  - JOUR
AU  - A. V. Kravchenko
TI  - On directed and finitely partitionable bases for quasi-identities
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 741
EP  - 746
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a3/
LA  - en
ID  - SEMR_2022_19_2_a3
ER  - 
%0 Journal Article
%A A. V. Kravchenko
%T On directed and finitely partitionable bases for quasi-identities
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 741-746
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a3/
%G en
%F SEMR_2022_19_2_a3
A. V. Kravchenko. On directed and finitely partitionable bases for quasi-identities. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 741-746. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a3/

[1] V.A. Gorbunov, A.V. Kravchenko, “Antivarieties and colour-families of graphs”, Algebra Univers., 46:1-2 (2001), 43–67 | DOI | MR | Zbl

[2] V.K. Kartashov, “Quasivarieties of unars”, Math. Notes, 27 (1980), 5–12 | DOI | MR | Zbl

[3] A.V. Kravchenko, A.M. Nurakunov, M.V. Schwidefsky, “Structure of quasivariety lattices. I: Independent axiomatizability”, Algebra Logic, 57:6 (2019), 445–462 | DOI | Zbl

[4] A.V. Kravchenko, A.M. Nurakunov, M.V. Schwidefsky, “Structure of quasivariety lattices. II: Undecidable problems”, Algebra Logic, 58:2 (2019), 123–136 | DOI | MR | Zbl

[5] A.V. Kravchenko, A.M. Nurakunov, M.V. Schwidefsky, “Structure of quasivariety lattices. III: Finitely partitionable bases”, Algebra Logic, 59:3 (2020), 222–229 | DOI | MR | Zbl

[6] A.V. Kravchenko, A.M. Nurakunov, M.V. Schwidefsky, “Structure of quasivariety lattices. IV: Nonstandard quasivarieties”, Sib. Math. J., 62:5 (2021), 850–858 | DOI | MR | Zbl

[7] A.I. Mal'tsev, “Universally axiomatizable subclasses of locally finite classes of models”, Sib. Math. J., 8 (1967), 764–770 | DOI | Zbl