Residuated Structures,Concentric Sums and Finiteness Conditions |
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Authors: | J. S. Olson |
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Affiliation: | Department of Mathematics , Norwich University , Northfield, Vermont, USA |
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Abstract: | This article is motivated by a concern with finiteness conditions on varieties of residuated structures—particularly residuated meet semilattice-ordered commutative monoids. A “concentric sum” construction is developed and is used to prove, among other results, a local finiteness theorem for a class that encompasses all n-potent hoops and all idempotent subdirect products of residuated chains. This in turn implies that a range of residuated lattice-based varieties have the finite embeddability property, whence their quasi-equational theories are decidable. Applications to substructural logics are discussed. |
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Keywords: | Decidability Finite embeddability property Hoop Locally finite variety Natural order Residuation Substructural logics |
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