Geodesic
On nonstandard quasivarieties of differential groupoids and unary algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 768-783.

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We prove that there are continuum many nonstandard quasivarieties of differential groupoids and unary algebras.
Keywords: quasivariety, nonstandard quasivariety, differential groupoid, unary algebra. 
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A. V. Kravchenko; M. V. Schwidefsky. On nonstandard quasivarieties of differential groupoids and unary algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 768-783. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a5/

[1] A.O. Basheyeva, M. Mustafa, A.M. Nurakunov, “Properties not retained by pointed enrichments of finite lattices”, Algebra Univers., 81:4 (2020), 56 | DOI | MR | Zbl

[2] A. Basheyeva, A.M. Nurakunov, M.V. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. Èlectron. Mat. Izv., 14 (2017), 252–263 | MR | Zbl

[3] D.M. Clark, B.A. Davey, Natural dualities for the working algebraist, Cambridge University Press, Cambridge, 1998 | MR | Zbl

[4] D.M. Clark, B.A. Davey, R.S. Freese, M. Jackson, “Standard topological algebras: syntactic and principal congruences and profiniteness”, Algebra Univers., 52:2-3 (2004), 343–376 | DOI | MR | Zbl

[5] D.M. Clark, B.A. Davey, M. Haviar, J.G. Pitkethly, M.R. Talukder, “Standard topological quasi-varieties”, Houston J. Math., 29:4 (2003), 859–887 | MR | Zbl

[6] D.M. Clark, B.A. Davey, M.G. Jackson, J.G. Pitkethly, “The axiomatizability of topological prevarieties”, Adv. Math., 218:5 (2008), 1604–1653 | DOI | MR | Zbl

[7] B.A. Davey, M. Jackson, M. Maróti, R.N. McKenzie, “Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties”, J. Aust. Math. Soc., 85:1 (2008), 59–74 | DOI | MR | Zbl

[8] V.A. Gorbunov, Algebraic theory of quasivarieties, Consultants Bureau, New York, 1998 | MR | Zbl

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

[10] P.T. Johnstone, Stone spaces, Cambridge University Press, Cambridge, 1982 | MR | Zbl

[11] A.V. Kravchenko, “Complexity of lattices of quasivarieties for varieties of unary algebras”, Sib. Adv. Math., 12:1 (2001), 63–76 | 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, “Complexity of quasivariety lattices for varieties of unary algebras. II”, Sib. Èlectron. Mat. Izv., 13 (2016), 388–394 | MR | Zbl

[14] A.V. Kravchenko, “On directed and finitely partitionable bases for quasi-identities”, Sib. Èlectron. Mat. Izv., 19 (2022) (to appear) | MR

[15] A.V. Kravchenko, M.V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. Èlectron. Mat. Izv., 17 (2020), 753–768 | DOI | MR | Zbl

[16] A.V. Kravchenko, A.M. Nurakunov, M.V. Schwidefsky, “Quasi-equational bases of differential groupoids and unary algebras”, Sib. Èlectron. Mat. Izv., 14 (2017), 1330–1337 | MR | Zbl

[17] 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

[18] 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

[19] 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

[20] 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

[21] A.M. Nurakunov, M.M. Stronkowski, “Profiniteness in finitely generated varieties is undecidable”, J. Symb. Log., 83:4 (2018), 1566–1578 | DOI | MR | Zbl

[22] L. Ribes, P. Zalesskii, Profinite groups, Springer, Berlin, 2000 | MR | Zbl

[23] A. Romanowska, B. Roszkowska, “On some groupoid modes”, Demonstr. Math., 20:1-2 (1987), 277–290 | MR | Zbl

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

[25] M.V. Schwidefsky, “Complexity of quasivariety lattices”, Algebra Logic, 54:3 (2015), 245–257 | DOI | MR | Zbl

[26] M.V. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. II”, Int. J. Algebra Comput., 24:8 (2014), 1099–1126 | DOI | MR | Zbl

[27] B. Trotta, “Residual properties of reflexive anti-symmetric digraphs”, Houston J. Math., 37:1 (2011), 27–46 | MR | Zbl