论文标题
双订单不是由总订单产生的
Bi-orders do not arise from total orders
论文作者
论文摘要
我们提出了一些有关组的双订单性的Zermelo-fraenkel一致性结果，以及构造具有conradian命令的群体，其每一个对公制空间的行动都限制了轨道。超级引理的经典后果是，只有当它是可局部生物订单时，一组是可以生命的。我们表明存在ZF的模型，其中有一个本地不含（ERGO局部双订单）而不是双级订单的组，并且可以为组提供总顺序。这种群体也可以在依赖选择原理的情况下存在。为无扭转的阿贝尔群体提供了可比的一致性结果。
We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well as a construction of groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence of the ultrafilter lemma is that a group is bi-orderable if and only if it is locally bi-orderable. We show that there exists a model of ZF in which there is a group which is locally free (ergo locally bi-orderable) and not bi-orderable, and the group can be given a total order. Such a group can also exist in the presence of the principle of dependent choices. Comparable consistency results are provided for torsion-free abelian groups.
