The isomorphism problem for finitely generated bi-orderable groups

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.

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