The isomorphism problem for finitely generated bi-orderable groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910199749541888 |
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| author | Calderoni, Filippo Clay, Adam |
| author_facet | Calderoni, Filippo Clay, Adam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The isomorphism problem for finitely generated bi-orderable groups Calderoni, Filippo Clay, Adam Group Theory Logic 03E15, 06F15, 20F60 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. |
| title | The isomorphism problem for finitely generated bi-orderable groups |
| topic | Group Theory Logic 03E15, 06F15, 20F60 |
| url | https://arxiv.org/abs/2510.10673 |