No CrossRef data available.
Article contents
Bi-orders do not arise from total orders
Published online by Cambridge University Press: 20 April 2021
Abstract
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.
MSC classification
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2021
Footnotes
This work was supported by the Severo Ochoa Program for Centres of Excellence in R&D SEV-20150554 and the Heilbronn Institute for Mathematical Research Bristol, UK.