通过布鲁克斯-拉克塞尔塔的连接分布度

arXiv - MATH - Logic Pub Date : 2024-09-07 DOI:arxiv-2409.04894

G. Bezhanishvili, F. Dashiell Jr, A. Moshier, J. Walters-Wayland

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引用次数: 0

摘要

我们利用布鲁克斯-拉克塞完备性引入了有界分布网格的布鲁克斯-拉克塞塔。这一机制使我们能够在有界分布网格类中发展出各种层次结构，这些层次结构度量了有界分布网格的分布度及其戴德金-麦克尼尔完备性。我们还利用普里斯特里对偶性得到了所得到的层次的对偶特征。除其他外，这还产生了埃萨基亚的海廷网格表征在海廷网格之上的自然广义化。

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Degrees of join-distributivity via Bruns-Lakser towers

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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arXiv - MATH - Logic

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