Representable idempotent commutative residuated lattices
James Raftery · Transactions of the American Mathematical Society · 2007
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.