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

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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.

Original languageEnglish
Pages (from-to)753-768
Number of pages16
JournalSiberian Electronic Mathematical Reports
Volume17
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Computable set
  • Congruence lattice
  • Differential groupoid
  • Quasivariety
  • Unary algebra
  • Undecidable problem
  • Variety

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