Nick Galatos, Xiao Zhuang
Published 2023-04-11Version 1
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.
Comments: 28 pages, 5 figures
Some problems with two axiomatizations of discussive logic
Filtrations for $\mathbb{wK4}$ and its relatives
Degrees of the finite model property: the antidichotomy theorem
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