On n-distality, n-triviality and hypergraph regularity in NIP theories
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911652405837824 |
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| author | Chernikov, Artem Westhead, Francis |
| author_facet | Chernikov, Artem Westhead, Francis |
| contents | We study Keisler measures in strongly n-distal NIP theories, generalizing some results of Simon and Chernikov-Starchenko for distal theories and addressing some questions of Walker. In particular, we establish a hypergraph version of the distal regularity lemma, compact domination for definable fsg groups, and demonstrate that the strong n-distality hierarchy is strict among stable theories using a connection to Poizat's total triviality of forking. We also show that infinite strongly n-distal NIP fields have characteristic 0 using a discrepancy result of Babai-Hayes-Kimmel from multiparty communication complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04714 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On n-distality, n-triviality and hypergraph regularity in NIP theories Chernikov, Artem Westhead, Francis Logic Combinatorics 03C45, 05C35, 05C65 We study Keisler measures in strongly n-distal NIP theories, generalizing some results of Simon and Chernikov-Starchenko for distal theories and addressing some questions of Walker. In particular, we establish a hypergraph version of the distal regularity lemma, compact domination for definable fsg groups, and demonstrate that the strong n-distality hierarchy is strict among stable theories using a connection to Poizat's total triviality of forking. We also show that infinite strongly n-distal NIP fields have characteristic 0 using a discrepancy result of Babai-Hayes-Kimmel from multiparty communication complexity. |
| title | On n-distality, n-triviality and hypergraph regularity in NIP theories |
| topic | Logic Combinatorics 03C45, 05C35, 05C65 |
| url | https://arxiv.org/abs/2605.04714 |