论文标题
一组本地订购的数量
The number of locally invariant orderings of a group
论文作者
论文摘要
我们表明，如果一个非平凡的群体承认本地不变的订单，那么它将承认许多本地不变的订单。对于左订单组的情况，我们为本地订购的不可数家庭提供明确的构造；对于一般组，我们提供了一个存在的定理，该定理应用紧凑性，以产生许多本地不变的订单。在此过程中，我们定义并研究了一个群体的本地订单，自然组对这个空间的自然行动以及它们与左顺序空间的关系。
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of locally invariant orderings; for a general group we provide an existence theorem that applies compactness to yield uncountably many locally invariant orderings. Along the way, we define and investigate the space of locally invariant orderings of a group, the natural group actions on this space, and their relationship to the space of left-orderings.
