Representable idempotent commutative residuated lattices

DOI10.1090/S0002-9947-07-04235-3zbMath1117.03070OpenAlexW1986245444MaRDI QIDQ3443137

James G. Raftery

Publication date: 31 May 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04235-3

zbMATH Keywords

idempotentrelevance logiclocally finite varietyresiduated latticerepresentableresiduationSugihara monoidminglerelative Stone algebra

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Ordered semigroups and monoids (06F05) Quasivarieties (08C15) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Varieties of lattices (06B20) Subdirect products and subdirect irreducibility (08B26)

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Cites Work

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• Positive Sugihara monoids
• The semantics and proof theory of linear logic
• Fragments of R-mingle
• Adding involution to residuated structures
• The finite embeddability property for residuated lattices, pocrims and BCK-algebras.
• On the lattice of quasivarieties of Sugihara algebras
• Equational bases for joins of residuated-lattice varieties
• Rule separation and embedding theorems for logics without weakening
• On the structure of varieties with equationally definable principal congruences. I
• On the structure of hoops
• Conservative extension in relevant implication
• Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL
• Subdirectly irreducible residuated semilattices and positive universal classes
• On conserving positive logics
• Minimal varieties of residuated lattices
• Constructing simple residuated lattices
• Algebraic Analysis of Many Valued Logics
• A propositional calculus with denumerable matrix
• A remark on the s. c. free closure algebras
• The finite model property for knotted extensions of propositional linear logic
• NONE OF THE VARIETY En, n>2, IS LOCALLY FINITE
• Algebraizable logics
• On formulas of one variable in intuitionistic propositional calculus
• THE STRUCTURE OF COMMUTATIVE RESIDUATED LATTICES
• On the finite embeddability property for residuated ordered groupoids
• Algebras Whose Congruence Lattices are Distributive.
• Algebraic completeness results for R-mingle and its extensions
• Independent Axioms for the Implicational Fragment of Sobociński's Three‐Valued Logic

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