Finite Basis Theorems for Relatively Congruence-Distributive Quasivarieties

DOI10.2307/2000978zbMath0706.08009OpenAlexW4238282572MaRDI QIDQ3487457

Don Pigozzi

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2000978

zbMATH Keywords

quasi-identitiesabstract data typesfinitely generatedfinite basis theoremquasivariety of generalized equality-test algebrasrelative subvarietyRelatively congruence-distributive quasivarieties

Mathematics Subject Classification ID

Abstract data types; algebraic specification (68Q65) Equational logic, Mal'tsev conditions (08B05) Quasivarieties (08C15) Equational classes, universal algebra in model theory (03C05)

Related Items (33)

Bjarni Jónsson's contributions in algebra ⋮ Finitely axiomatizable quasivarieties of graphs ⋮ Gentzen-style axiomatizations in equational logic ⋮ Quasi-identities of finite semigroups and symbolic dynamics ⋮ Structure of lattices of varieties and lattices of quasivarieties: Similarity and difference. I ⋮ Relation formulas for protoalgebraic equality free quasivarieties; Pałasińska's theorem revisited ⋮ A Mathematical Life ⋮ The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras ⋮ Relatively congruence modular quasivarieties of modules ⋮ Relative congruence formulas and decompositions in quasivarieties ⋮ The algebraic significance of weak excluded middle laws ⋮ Universal algebraic methods for non-classical logics ⋮ Abstract algebraic logic. An introductory chapter ⋮ Least \(V\)-quasivarieties of MV-algebras ⋮ Anshakov-Rychkov algebras ⋮ Baker–Pixley theorem for algebras in relatively congruence distributive quasivarieties ⋮ Properties not retained by pointed enrichments of finite lattices ⋮ Triangular irreducibility of congruences in quasivarieties ⋮ Finite bases for finitely generated, relatively congruence distributive quasivarities ⋮ Inconsistency lemmas in algebraic logic ⋮ A single quasi-identity for a quasivariety with the Fraser-Horn property ⋮ Characterization of relatively distributed quasivarieties of algebras ⋮ An answer to a question of D. Pigozzi ⋮ Quasivarieties of distributive \(p\)-algebras ⋮ Finite basis problems and results for quasivarieties ⋮ Commutator Theory for Relatively Modular Quasivarieties ⋮ Quasivarieties of algebras with definable principal congruences ⋮ Semisimplicity and the discriminator in bounded BCK-algebras ⋮ Quasiequational Theories of Flat Algebras ⋮ On finitely based groups and nonfinitely based quasivarieties ⋮ Quasivarieties with definable relative principal subcongruences ⋮ Semiconic idempotent residuated structures ⋮ A quasi-Mal'cev condition with unexpected application.

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