Unilinear residuated lattices: axiomatization, varieties and FEP

2023/04/11 by Galatos, Nick, Zhuang, Xiao
#03B47 #03G10 (secondary) #06F05 (primary) 08B15 #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2304.05508

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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