Representable idempotent commutative residuated lattices

Raftery, J.

doi:10.1090/S0002-9947-07-04235-3

Representable idempotent commutative residuated lattices
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by J. G. Raftery PDF

Trans. Amer. Math. Soc. 359 (2007), 4405-4427 Request permission

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 $\mbox {mingle}$ and Gödel-Dummett axioms has a solvable deducibility problem.

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