论文标题
在局部有限的矫形格
On locally finite orthomodular lattices
论文作者
论文摘要
让我们用LF表示局部有限的所有原始晶格（OML）的类别（即，LF中的L提供了L l a的每个有限子集中的每个有限子集，该子集中在l a a a A a A A a A a有限的子OML中产生）。我们首先在本注中显示如何从初始oml中获得新的局部有限的OML并放大，从而将LF类获取。但是，显然，我们发现LF很大，并非所有OML都属于LF。然后，我们研究了LF的OML。我们表明，本地有限可能在一定程度上弥补了分配的弥补。例如，我们表明，如果l在lf中，如果对于任何有限的子k，则在k上有一个状态s：k至[0，1]，则整个L上有一个状态。我们还考虑了LF的进一步代数和状态与量子逻辑理论相关的态度。
Let us denote by LF the class of all orthomodular lattices (OMLs) that are locally finite (i.e., L in LF provided each finite subset of L generates in L a finite subOML). We first show in this note how one can obtain new locally finite OMLs from the initial ones and enlarge thus the class LF . We find LF considerably large though, obviously, not all OMLs belong to LF . We then study states on the OMLs of LF . We show that local finiteness may to a certain extent make up for distributivity. We for instance show that if L in LF and if for any finite subOML K there is a state s : K to [0, 1] on K, then there is a state on the entire L. We also consider further algebraic and state properties of LF relevant to quantum logic theory.
