A dichotomy for countable unions of smooth Borel equivalence relations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909461366439936 |
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| author | de Rancourt, N. Miller, B. D. |
| author_facet | de Rancourt, N. Miller, B. D. |
| contents | We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a Polish space or a continuous embedding of $\mathbb{E}_1$ into $E$. We also establish related results concerning countable unions of more general Borel equivalence relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05362 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A dichotomy for countable unions of smooth Borel equivalence relations de Rancourt, N. Miller, B. D. Logic Primary 03E15, 28A05 We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a Polish space or a continuous embedding of $\mathbb{E}_1$ into $E$. We also establish related results concerning countable unions of more general Borel equivalence relations. |
| title | A dichotomy for countable unions of smooth Borel equivalence relations |
| topic | Logic Primary 03E15, 28A05 |
| url | https://arxiv.org/abs/2105.05362 |