A finite basis theorem for residually finite, congruence meet-semidistributive varieties

DOI10.2307/2586531zbMath0973.08004arXivmath/9712291OpenAlexW2594244112MaRDI QIDQ4953214

Ross Willard

Publication date: 5 December 2001

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9712291

zbMATH Keywords

equational theoryresidual boundfinite basis theoremresidually small varietiescongruence meet-semidistributive varieties

Mathematics Subject Classification ID

Equational logic, Mal'tsev conditions (08B05) Congruence modularity, congruence distributivity (08B10) Equational classes, universal algebra in model theory (03C05)

Related Items (20)

Inherently nonfinitely based lattices ⋮ Identities and quasi-identities of pointed algebras ⋮ The variety generated by \(\mathbb {A}(\mathcal {T})\) -- two counterexamples ⋮ Optimal strong Mal'cev conditions for congruence meet-semidistributivity in locally finite varieties ⋮ Congruence meet-semidistributive locally finite varieties and a finite basis theorem ⋮ Relatively congruence modular quasivarieties of modules ⋮ Simpler Maltsev conditions for (weak) difference terms in locally finite varieties ⋮ Universal algebraic methods for non-classical logics ⋮ Triangular irreducibility of congruences in quasivarieties ⋮ A juggler's dozen of easy\(^\dag\) problems (\(^\dag\) Well, easily formulated \dots). ⋮ Mal'tsev conditions, lack of absorption, and solvability. ⋮ Maltsev families of varieties closed under join or Maltsev product ⋮ A characterization of idempotent strong Mal'cev conditions for congruence meet-semidistributivity in locally finite varieties ⋮ Fragments of R-mingle ⋮ Finite basis problems and results for quasivarieties ⋮ A finite basis theorem for difference-term varieties with a finite residual bound ⋮ Finite bases for flat graph algebras ⋮ Deciding active structural completeness ⋮ Quasivarieties with definable relative principal subcongruences ⋮ A quasi-Mal'cev condition with unexpected application.

Cites Work

• Finite equational bases for congruence modular varieties
• Finite equational bases for finite algebras in a congruence-distributive equational class
• Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties
• Residually small varieties
• Semi-categorial algebras. II
• A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive
• Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound
• Tarski’s finite basis problem via 𝐀(𝒯)
• The Relationship Between Two Commutators
• THE RESIDUAL BOUNDS OF FINITE ALGEBRAS
• THE RESIDUAL BOUND OF A FINITE ALGEBRA IS NOT COMPUTABLE
• TARSKI’S FINITE BASIS PROBLEM IS UNDECIDABLE
• Algebras Whose Congruence Lattices are Distributive.

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