Representable idempotent commutative residuated lattices

• Autores: James G. Raftery
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 9, 2007, págs. 4405-4427
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04235-3
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• Resumen

  • It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of positive relevance logic containing the mingle and Gödel-Dummett axioms has a solvable deducibility problem.