The isomorphism problem for finitely generated bi-orderable groups
Group Theory
2026-05-11 v2 Logic
Abstract
We analyze the classification problem for finitely generated orderable groups from the viewpoint of descriptive set theory. We analyze the standard Borel space of finitely generated left-orderable groups, and the subspace of finitely generated bi-orderable groups using spaces of relative cones. We use this setup to show that the isomorphism relation on finitely generated bi-orderable groups is weakly universal.
Cite
@article{arxiv.2510.10673,
title = {The isomorphism problem for finitely generated bi-orderable groups},
author = {Filippo Calderoni and Adam Clay},
journal= {arXiv preprint arXiv:2510.10673},
year = {2026}
}
Comments
17 pages. We reworked Section 2, where we fixed a mistake from the previous version. We revised the rest of the paper accordingly. The main result is not affected by the revision