正规格展开式的对偶性和带关系的排序残馀框架

IF 0.6 4区 数学 Q3 MATHEMATICS
Chrysafis Hartonas
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引用次数: 2

摘要

我们重新讨论了具有拟算子的格的Stone对偶问题,给出了一个新的对偶结果。新的结果在两个重要方面比我们以前的工作有所改进。首先,现在简化了框架的公理化,部分是通过结合Gehrke关于关系的截面稳定性的建议。其次,对态射进行了重新定义,以保持Galois稳定(和共稳定)集,我们再次部分依赖于Goldblatt最近提出的极性有界态射的定义。在研究与具有关系的极性相关的对偶代数结构时,我们证明了稳定/共稳定集算子是由框架关系生成的经典(尽管排序)图像算子对Galois稳定/共稳集的限制的Galois闭包。这在表示层面上证明了非分配逻辑可以被视为排序剩余(多)模态逻辑的片段,这是作者最近提出的一个研究方向。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Duality for normal lattice expansions and sorted residuated frames with relations

We revisit the problem of Stone duality for lattices with quasioperators, presenting a fresh duality result. The new result is an improvement over that of our previous work in two important respects. First, the axiomatization of frames is now simplified, partly by incorporating Gehrke’s proposal of section stability for relations. Second, morphisms are redefined so as to preserve Galois stable (and co-stable) sets and we rely for this, partly again, on Goldblatt’s recently proposed definition of bounded morphisms for polarities. In studying the dual algebraic structures associated to polarities with relations we demonstrate that stable/co-stable set operators result as the Galois closure of the restriction of classical (though sorted) image operators generated by the frame relations to Galois stable/co-stable sets. This provides a proof, at the representation level, that non-distributive logics can be regarded as fragments of sorted residuated (poly)modal logics, a research direction recently initiated by this author.

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来源期刊
Algebra Universalis
Algebra Universalis 数学-数学
CiteScore
1.00
自引率
16.70%
发文量
34
审稿时长
3 months
期刊介绍: Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
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