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arXiv · 2510.10673

The isomorphism problem for finitely generated bi-orderable groups

Filippo Calderoni·Adam Clay
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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.

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Filippo Calderoni, Adam Clay. 2025-10-12. The isomorphism problem for finitely generated bi-orderable groups. https://arxiv.org/abs/2510.10673

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