This article is cited in 8 papers

Mathematical logic, algebra and number theory

On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras

A. V. Kravchenko^abcd, M. V. Schwidefsky<sup>abd

a</sup> Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
^c Siberian Institute of Management, 6, Nizhegorodskaya str., Novosibirsk, 630102, Russia
^d Novosibirsk State Technical University, 20, Karl Marx ave.., Novosibirsk, 630073, Russia

Abstract: 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.

UDC: 512.57

MSC: 08C15, 03C05

Received November 19, 2019, published June 4, 2020

Language: English

DOI: 10.33048/semi.2020.17.054

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