Structure of quasivariety lattices. II: Undecidable problems
type: Item
instance of: scholarly article
title: Structure of quasivariety lattices. II: Undecidable problems
zbMATH Open document ID: 1444.08005
published in: Algebra and Logic
publication date: 2019-12-06T00:00:00Z
review text: The paper provides sufficient conditions for a quasivariety \(\mathbf M\) to contain continuumly many subquasivarieties \(\mathbf K\) such that the membership problem for finitely presented structures in \(\mathbf M\) is undecidable in \(\mathbf K\), the finite membership problem is undecidable in \(\mathbf K\), the quasi-equational theory of \(\mathbf K\) is undecidable, and \(\mathbf K\) has an independent quasi-equational basis relative to \(\mathbf M\). Some applications are presented. For Part I see [the authors, Algebra Logic 57, No. 6, 445--462 (2019; Zbl 1439.08008); translation from Algebra Logika 57, No. 6, 684--710 (2018)].
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 7140976
zbMATH Keywords: quasi-identity
zbMATH Keywords: quasivariety
zbMATH Keywords: membership problem
zbMATH Keywords: undecidable theory
zbMATH Keywords: independent basis
zbMATH Keywords: \(Q\)-universality
author: Aleksandr Vladimirovich Kravchenko
author: A. M. Nurakunov
author: M. V. Schwidefsky
reviewed by: Keith A. Kearnes
MaRDI profile type: Publication
full work available at URL: s10469-019-09531-5
OpenAlex ID: W2962870656
cites work: Structure of quasivariety lattices. I: Independent axiomatizability
cites work: Lattices of subclasses. III
cites work: Q5628181
cites work: Q4935937
cites work: Quasivarieties of unary algebras with a finite number of cycles
cites work: Quasivarieties of graphs
cites work: Covers in lattices of quasivarieties and independent axiomatizability
cites work: Q3565123
cites work: Q4369483
cites work: Q-Universal Quasivarieties of Algebras
cites work: Quasivarieties of Cantor algebras.
cites work: Quasivariety lattices of pointed abelian groups.
cites work: Projective Geometries as Projective Modular Lattices
cites work: Q4165426
cites work: Finite-to-finite universal quasivarieties are \(Q\)-universal.
cites work: Universal Varieties Of (0, 1)-Lattices
cites work: The lattice of quasivarieties of undirected graphs.
cites work: Q4677700
cites work: Q4517140
cites work: Q3697064
cites work: Quasivarieties of Graphs and Independent Axiomatizability
cites work: On quasi-equational bases for differential groupoids and unary algebras
cites work: Complexity of quasivariety lattices for varieties of unary algebras. II.
cites work: Q4789441
cites work: Q4406616
cites work: Q4532126
cites work: Complexity of quasivariety lattices for varieties of differential groupoids
cites work: Complexity of quasivariety lattices.
cites work: Unreasonable lattices of quasivarieties
DOI: 10.1007/S10469-019-09531-5
description: scientific article; zbMATH DE number 7140976