通过Bruns-Lakser塔的联合分配度

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series Pub Date : 2025-03-11 DOI:10.1016/j.indag.2025.02.005

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

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引用次数: 0

摘要

我们利用Bruns-Lakser完成引入Bruns-Lakser塔楼的半格子结构。这种机制使我们能够在有界分布格类中发展各种层次结构，这些层次结构测量有界分布格的分布度及其Dedekind-MacNeille补全。我们还使用普利斯特利对偶性来获得所得层次的对偶特征。除此之外，这产生了Esakia的Heyting格表示到proHeyting格的自然推广。

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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

κ

-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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来源期刊

Indagationes Mathematicae-New Series 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

79 days

期刊介绍： Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.