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On the Independent Axiomatizability of Quasivarieties of Nilpotent Groups
Siberian mathematical journal, 2023A. Budkin
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2001
This chapter plays a twofold role in the book. Firstly, the chapter surveys basic facts about quasivarieties of algebras. These facts are widely utilised in the subsequent chapters devoted to algebraizable logics. Secondly, the chapter shows how the methods initially elaborated for protoalgebraic sentential logics in the first part can be also applied ...
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This chapter plays a twofold role in the book. Firstly, the chapter surveys basic facts about quasivarieties of algebras. These facts are widely utilised in the subsequent chapters devoted to algebraizable logics. Secondly, the chapter shows how the methods initially elaborated for protoalgebraic sentential logics in the first part can be also applied ...
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Subquasivarieties of implicative locally‐finite quasivarieties
Mathematical Logic Quarterly, 2010AbstractA quasivariety is said to be implicative if it is generated by a class of algebras with equationally‐definable implication of equalities. Implicative finitely‐generated quasivarieties appear naturally within logic, for instance, as equivalent quasivarieties of Gentzen‐style calculi for finitely‐valued propositional logics with equality ...
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Coverings in the lattice of quasivarieties of ℓ-groups
Siberian Mathematical Journal, 1992See the review in Zbl 0772.06013.
Isaeva, O. V., Medvedev, N. Ya.
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Levi Classes of Quasivarieties of Nilpotent Groups of Exponent ps
Algebra i logika, 2022V. V. Lodeishchikova, S. M. Shakhova
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Quasivarieties of equivalential algebras
Reports Math. Log., 1995Summary: The expressive power of constants in the quasi-equational logic is considered. We describe three 3-element algebras \(A_1, A_2, A_3\) such that \(A_{i+1}\) is obtained from \(A_i\) by adding one constant to the signature and such that the quasivariety generated by \(A_2\) has infinitely many subquasivarieties, while both \(A_1\) and \(A_3 ...
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Sequent calculi and quasivarieties
Reports Math. Log., 2000Summary: We discuss relatively point-regular quasivarieties related in some special sense to sequent calculi. We show that the free algebra in such a quasivariety is Fregean iff in the sequent calculus the so-called symmetric contraction rules are admissible. In the presence of the fusion connective this is equivalent to having contraction.
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Dominions in quasivarieties of universal algebras
Studia Logica, 2004Let \(\mathcal M\) be a class of algebras, and let \(H\) be a subalgebra of the algebra \(A\), then the dominion of \(H\) in \(A\) (in a class \(\mathcal M\)) is defined by: \[ \text{dom}^{\mathcal M}_A(H)=\{a\in A\mid \forall M\in {\mathcal M}, \forall f,g : A\to M (f| _h=g| _g \Rightarrow a^f=a^g)\}.
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Independent Axiomatizability of Quasivarieties of Torsion-Free Nilpotent Groups
Algebra i logika, 2021A. Budkin
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On the axiomatic ranks of some quasivarieties
Siberian Mathematical Journal, 1999The author studies the axiomatic rank of quasivarieties of torsion-free nilpotent groups of class at most \(2\). Theorem 1. There are no quasivarieties of torsion-free nilpotent groups of class at most \(2\) which have axiomatic rank equal to \(3\).
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