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arXiv · 2304.05508

Unilinear residuated lattices: axiomatization, varieties and FEP

Nick Galatos·Xiao Zhuang
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Abstract

We characterize all residuated lattices that have height equal to $3$ and show that the variety they generate has continuum-many subvarieties. More generally, we study unilinear residuated lattices: their lattice is a union of disjoint incomparable chains, with bounds added. We we give two general constructions of unilinear residuated lattices, provide an axiomatization and a proof-theoretic calculus for the variety they generate, and prove the finite model property for various subvarieties.

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Nick Galatos, Xiao Zhuang. 2023-04-11. Unilinear residuated lattices: axiomatization, varieties and FEP. https://arxiv.org/abs/2304.05508

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