论文标题
分段伪安装的晶格和Posets的过滤器和一致性
Filters and congruences in sectionally pseudocomplemented lattices and posets
论文作者
论文摘要
在我们以前的论文中，我们与J. Paseka一起引入了所谓的截面拟合晶格和posets，并照亮了它们在代数结构中的作用。我们认为，类似于相对伪安装的晶格 - 这些结构可以用作某些直觉逻辑的代数语义。本文的目的是定义这些结构中的一致性和过滤器，得出它们之间的相互关系，并描述强烈伪造的POSET中一致性的基本特性。为了描述过滤器，既有分段伪安装的晶格和posets，我们使用A. Ursini引入的工具，即相对于它们的理想术语和封闭性。尽管相应的理想术语并非到处定义，但似乎也可以将类似的机械应用于强烈的伪安装posets，这似乎具有某种兴趣。
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented lattices - these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters both in sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e. ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.
