On large externally definable sets in NIP
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866915025159979008 |
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| author | Bays, Martin Ben-Neria, Omer Kaplan, Itay Simon, Pierre |
| author_facet | Bays, Martin Ben-Neria, Omer Kaplan, Itay Simon, Pierre |
| contents | We study cofinal systems of finite subsets of $ω_1$. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: in an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11792 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On large externally definable sets in NIP Bays, Martin Ben-Neria, Omer Kaplan, Itay Simon, Pierre Logic 03C45 We study cofinal systems of finite subsets of $ω_1$. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: in an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals. |
| title | On large externally definable sets in NIP |
| topic | Logic 03C45 |
| url | https://arxiv.org/abs/2205.11792 |