A Borel graphable equivalence relation with no Borel graphing of diameter two
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909984354205696 |
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| author | Lutz, Patrick |
| author_facet | Lutz, Patrick |
| contents | We answer a question of Arant, Kechris and Lutz by showing that there is a Borel graphable equivalence relation with no Borel graphing of diameter less than 3. More specifically, we prove that there is an equivalence relation with a Borel graphing of diameter at most 4 but no Borel graphing of diameter less than 3. Our proof relies on a technical lemma about computability-theoretic genericity, which may have other applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04417 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Borel graphable equivalence relation with no Borel graphing of diameter two Lutz, Patrick Logic We answer a question of Arant, Kechris and Lutz by showing that there is a Borel graphable equivalence relation with no Borel graphing of diameter less than 3. More specifically, we prove that there is an equivalence relation with a Borel graphing of diameter at most 4 but no Borel graphing of diameter less than 3. Our proof relies on a technical lemma about computability-theoretic genericity, which may have other applications. |
| title | A Borel graphable equivalence relation with no Borel graphing of diameter two |
| topic | Logic |
| url | https://arxiv.org/abs/2601.04417 |