Borel Complexity of the Isomorphism Relation of Archimedean Orders in Finitely Generated Groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929281139998720 |
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| author | Poulin, Antoine |
| author_facet | Poulin, Antoine |
| contents | In 2020, Calderoni, Marker, Motto Ros and Shani asked what the Borel complexity of the isomorphism relation of Archimedean orders on $\mathbb{Q}^n$ is. We answer this question by proving that the isomorphism relation of Archimedean orders on $\mathbb{Z}^n$ is not hyperfinite when $n \geq 3$ and not treeable when $n \geq 4$. As a corollary, we get that the isomorphism relation of Archimedean orders on $\mathbb{Q}^n$ is not hyperfinite when $n \geq 3$ and not treeable when $n \geq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Borel Complexity of the Isomorphism Relation of Archimedean Orders in Finitely Generated Groups Poulin, Antoine Logic Dynamical Systems Group Theory In 2020, Calderoni, Marker, Motto Ros and Shani asked what the Borel complexity of the isomorphism relation of Archimedean orders on $\mathbb{Q}^n$ is. We answer this question by proving that the isomorphism relation of Archimedean orders on $\mathbb{Z}^n$ is not hyperfinite when $n \geq 3$ and not treeable when $n \geq 4$. As a corollary, we get that the isomorphism relation of Archimedean orders on $\mathbb{Q}^n$ is not hyperfinite when $n \geq 3$ and not treeable when $n \geq 4$. |
| title | Borel Complexity of the Isomorphism Relation of Archimedean Orders in Finitely Generated Groups |
| topic | Logic Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2403.11326 |