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On Set-Representable Orthocomplemented Difference Lattices
Order ( IF 0.6 ) Pub Date : 2020-03-03 , DOI: 10.1007/s11083-020-09522-7
Jianning Su

Matoušek introduced and axiomatized a notion of symmetric difference for orthocomplemented lattices (OMLs) called the orthocomplemented difference lattics ( ODLs ). We focus on the class of all ODLs that are set-representable and prove that this class is not locally finite by constructing an infinite three-generated set-representable ODL. This result answers a question posed by Matoušek and Pták. We also prove, by example, that not every concrete OML can be OML-embedded into an ODL.

中文翻译:

关于可表示的正交互补差分格

Matoušek 引入并公理化了正交互补格 (OML) 的对称差分概念,称为正交互补差分格 (ODL)。我们关注所有可集合表示的 ODL 的类,并通过构造一个无限的三个生成的可表示集合 ODL 来证明该类不是局部有限的。该结果回答了 Matoušek 和 Pták 提出的问题。我们还通过示例证明,并非每个具体的 OML 都可以将 OML 嵌入到 ODL 中。
更新日期:2020-03-03
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