通过Bruns-Lakser塔刻画的联合分配度
Degrees of join-distributivity via Bruns-Lakser towers
AI总结：
该研究借助Bruns-Lakser完备化提出交半格的Bruns-Lakser塔，构建有界分配格的κ-分配度层级，通过Priestley对偶性给出对偶刻画，并将Esakia的Heyting格表示推广至proHeyting格。
摘要：
我们利用Bruns-Lakser完备化引入了交半格的Bruns-Lakser塔。这一工具使我们得以在有界分配格类中构建多种层级结构，用于衡量有界分配格及其Dedekind-MacNeille完备化的κ-分配度。我们还运用Priestley对偶性得到了所得层级的对偶刻画。此外，这一工作将Esakia对Heyting格的表示自然推广到了proHeyting格。
英文摘要：
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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