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ISSN 1088-6850(e) ISSN 0002-9947(p)

Representable idempotent commutative residuated lattices

Author(s): J. G. Raftery
Journal: Trans. Amer. Math. Soc. 359 (2007), 4405-4427.
MSC (2000): Primary 03B47, 03G25, 06D99, 06F05, 08A50, 08C15
Posted: March 20, 2007
MathSciNet review: 2309191
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Abstract: It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The -generated subdirectly irreducible algebras in this variety are shown to have at most 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.

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