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Representable idempotent commutative residuated lattices


Author: J. G. Raftery
Journal: Trans. Amer. Math. Soc. 359 (2007), 4405-4427
MSC (2000): Primary 03B47, 03G25, 06D99, 06F05, 08A50, 08C15
DOI: https://doi.org/10.1090/S0002-9947-07-04235-3
Published electronically: 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 $ 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.


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Additional Information

J. G. Raftery
Affiliation: School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4001, South Africa
Email: raftery@ukzn.ac.za

DOI: https://doi.org/10.1090/S0002-9947-07-04235-3
Keywords: Locally finite variety, residuation, residuated lattice, representable, idempotent, Sugihara monoid, relative Stone algebra, relevance logic, mingle.
Received by editor(s): September 25, 2005
Published electronically: March 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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