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Bi-orders do not arise from total orders
Canadian Mathematical Bulletin ( IF 0.5 ) Pub Date : 2021-04-20 , DOI: 10.4153/s0008439521000229
Samuel M. Corson 1
Affiliation  

We present a Zermelo–Fraenkel ( $\textbf {ZF}$ ) consistency result regarding bi-orderability of groups. 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 $\textbf {ZF}$ plus dependent choice 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. The model also includes a torsion-free abelian group which is not bi-orderable but can be given a total order.



中文翻译:

双订单不是从总订单中产生的

我们提出了关于组的双序性的 Zermelo-Fraenkel ( $\textbf {ZF}$ ) 一致性结果。超滤引理的一个经典结果是,当且仅当它是局部双序的时,一个群是双序的。我们证明存在 $\textbf {ZF}$ 加上依赖选择的模型,其中存在一个局部自由(因此局部双序)且不可双序的组,并且可以给该组一个全序. 该模型还包括一个无扭阿贝尔群,它不是双阶的,但可以给定一个全阶。

更新日期:2021-04-20
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