Ramsey regularity implies no MAD families without uniformization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918164079575040 |
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| author | He, Jialiang Luo, Jintao Zhang, Shuguo |
| author_facet | He, Jialiang Luo, Jintao Zhang, Shuguo |
| contents | We show that if the Ramsey property holds (in a class of sets), then there is no MAD family (in this class, provided it satisfies some modest closure properties), proving a conjecture made by A.R.D.\ Mathias in 1977. As the technique we introduce for this proof is useful in a variety of related problems, we take the opportunity to announce 4 theorems, which will be proved in a follow-up paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ramsey regularity implies no MAD families without uniformization He, Jialiang Luo, Jintao Zhang, Shuguo Logic 03E15 We show that if the Ramsey property holds (in a class of sets), then there is no MAD family (in this class, provided it satisfies some modest closure properties), proving a conjecture made by A.R.D.\ Mathias in 1977. As the technique we introduce for this proof is useful in a variety of related problems, we take the opportunity to announce 4 theorems, which will be proved in a follow-up paper. |
| title | Ramsey regularity implies no MAD families without uniformization |
| topic | Logic 03E15 |
| url | https://arxiv.org/abs/2510.17399 |