Geodesic
On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 753-768

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We prove that certain lattices can be represented as the lattices of relative subvarieties and relative congruences of differential groupoids and unary algebras. This representation result implies that there are continuum many quasivarieties of differential groupoids such that the sets of isomorphism types of finite sublattices of their lattices of relative subvarieties and congruences are not computable. A similar result is obtained for unary algebras and their lattices of relative congruences.
Keywords: quasivariety, variety, congruence lattice, differential groupoid, unary algebra, undecidable problem, computable set. 
@article{SEMR_2020_17_a14,
     author = {A. V. Kravchenko and M. V. Schwidefsky},
     title = {On the complexity of the lattices of subvarieties and congruences. {II.} {Differential} groupoids and unary algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {753--768},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a14/}
}
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A. V. Kravchenko; M. V. Schwidefsky. On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 753-768. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a14/