Nurakunov, A. M. Quasi-identities of congruence-distributive quasivarieties of algebras. (English. Russian original) Zbl 0966.08010 Sib. Math. J. 42, No. 1, 108-118 (2001); translation from Sib. Mat. Zh. 42, No. 1, 123-135 (2001). Theorem 1. Let \(R\) be a congruence-distributive quasivariety of algebras of finite signature whose class of finitely subdirect \(R\)-indecomposable algebras is finitely axiomatizable. Then there exists a finite number \(n\) (depending on \(R\)) such that, if the congruence lattice of the \(R\)-free algebra of rank \(n\) has at most countable width or satisfies the minimality or maximality condition then \(R\) has a finite quasi-identities basis.Theorem 2. Assume \(K\) is a congruence-distributive quasivariety of algebras of finite signature, \(R=K\cap V\), where \(V\) is a variety of algebras, and the class of finitely subdirect \(R\)-indecomposable algebras is finitely axiomatizable. Then \(R\) is finitely axiomatizable with respect to \(K\). Reviewer: A.S.Morozov (Novosibirsk) Cited in 3 Documents MSC: 08C15 Quasivarieties Keywords:congruence-distributive quasivariety; quasi-identity; finitely subdirect indecomposable algebra; finitely axiomatizable class of algebras; finite basis PDFBibTeX XMLCite \textit{A. M. Nurakunov}, Sib. Math. J. 42, No. 1, 123--135 (2001; Zbl 0966.08010); translation from Sib. Mat. Zh. 42, No. 1, 123--135 (2001) Full Text: DOI EuDML