Structure of quasivariety lattices. II: Undecidable problems
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)].
scientific article; zbMATH DE number 7140976
scientific article