Degrees of join-distributivity via Bruns-Lakser towers
Logic
2025-03-26 v2
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 -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.
Keywords
Cite
@article{arxiv.2409.04894,
title = {Degrees of join-distributivity via Bruns-Lakser towers},
author = {G. Bezhanishvili and F. Dashiell and M. A. Moshier and J. Walters-Wayland},
journal= {arXiv preprint arXiv:2409.04894},
year = {2025}
}