论文标题
与Posets关联的正交性空间
Orthogonality spaces associated with posets
论文作者
论文摘要
正交性空间是配备了一种称为正交性的对称，反射性关系的集合。每个正交性空间都有相关的完整矫形器，称为正交空间的逻辑。对于每个POSET，我们将配备有一定正交性关系的正交性（这意味着，nonsingleton封闭间隔）关联。我们证明，有限的有限端位是一个晶格，并且仅当其正交性空间的逻辑是一个正交的晶格时。我们证明，当且仅当相关正交空间的逻辑是布尔代数时，且仅当Poset是链条。
An orthogonality space is a set equipped with a symmetric, irreflexive relation called orthogonality. Every orthogonality space has an associated complete ortholattice, called the logic of the orthogonality space. To every poset, we associate an orthogonality space consisting of proper quotients (that means, nonsingleton closed intervals), equipped with a certain orthogonality relation. We prove that a finite bounded poset is a lattice if and only if the logic of its orthogonality space is an orthomodular lattice. We prove that that a poset is a chain if and only if the logic of the associated orthogonality space is a Boolean algebra.
