Subdirectly Irreducible Residuated Semilattices and Positive Universal Classes |
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| Authors: | Jeffrey S. Olson |
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| Affiliation: | (1) Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 801 S. Morgan St., Chicago, 60608, IL, USA |
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| Abstract: | CRS(fc) denotes the variety of commutative residuated semilattice-ordered monoids that satisfy (x ⋀ e)k ≤ (x ⋀ e)k+1. A structural characterization of the subdi-rectly irreducible members of CRS(k) is proved, and is then used to provide a constructive approach to the axiomatization of varieties generated by positive universal subclasses of CRS(k). Dedicated to the memory of Willem Johannes Blok |
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| Keywords: | Residuation residuated lattices contraction linear logic positive universal formulas subdirectly irreducible algebras |
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