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  1. Quasivarieties with Definable Relative Principal Subcongruences.Anvar M. Nurakunov & M. M. Stronkowski - 2009 - Studia Logica 92 (1):109-120.
    For quasivarieties of algebras, we consider the property of having definable relative principal subcongruences, a generalization of the concepts of definable relative principal congruences and definable principal subcongruences. We prove that a quasivariety of algebras with definable relative principal subcongruences has a finite quasiequational basis if and only if the class of its relative (finitely) subdirectly irreducible algebras is strictly elementary. Since a finitely generated relatively congruence-distributive quasivariety has definable relative principal subcongruences, we get a new proof of the result (...)
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  • Finite basis problems and results for quasivarieties.Miklós Maróti & Ralph McKenzie - 2004 - Studia Logica 78 (1-2):293 - 320.
    Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection 1 of finite algebras of the same signature, , such that SP( 1) is finitely axiomatizable.We show also that if , then SP( 1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract (...)
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  • Inherently nonfinitely based lattices.Ralph Freese, George F. McNulty & J. B. Nation - 2002 - Annals of Pure and Applied Logic 115 (1-3):175-193.
    We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose equational theory is not finitely axiomatizable.
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  • Fragments of R-Mingle.W. J. Blok & J. G. Raftery - 2004 - Studia Logica 78 (1-2):59-106.
    The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of (...)
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