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arXiv · 2409.04894

Degrees of join-distributivity via Bruns-Lakser towers

G. Bezhanishvili·F. Dashiell Jr·M. A. Moshier·J. Walters-Wayland
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Abstract

We utilize the Bruns-Lakser completion to introduce Bruns-Lakser towers of a meet-semilattice. This machinery enables us to develop various hierarchies inside the class of bounded distributive lattices, which measure $\kappa$-degrees of distributivity of bounded distributive lattices and their Dedekind-MacNeille completions. We also use Priestley duality to obtain a dual characterization of the resulting hierarchies. Among other things, this yields a natural generalization of Esakia's representation of Heyting lattices to proHeyting lattices.

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G. Bezhanishvili, F. Dashiell Jr, M. A. Moshier, J. Walters-Wayland. 2024-09-07. Degrees of join-distributivity via Bruns-Lakser towers. https://arxiv.org/abs/2409.04894

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