Journal article
On large externally definable sets in NIP
- Abstract:
- We study cofinal systems of finite subsets of ω1. 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 314.3KB, Terms of use)
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- Publisher copy:
- 10.1017/S1474748023000464
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Journal of the Institute of Mathematics of Jussieu More from this journal
- Volume:
- 23
- Issue:
- 5
- Pages:
- 2159 - 2173
- Publication date:
- 2023-12-04
- Acceptance date:
- 2023-10-30
- DOI:
- EISSN:
-
1475-3030
- ISSN:
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1474-7480
- Language:
-
English
- Keywords:
- Pubs id:
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1570232
- Local pid:
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pubs:1570232
- Deposit date:
-
2023-11-24
- ARK identifier:
Terms of use
- Copyright holder:
- Bays et al.
- Copyright date:
- 2023
- Rights statement:
- © The Author(s), 2023. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (https://creativecommons.org/licenses/by-nc-sa/4.0), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is used to distribute the reused or adapted article and the original article is properly cited. The written permission of Cambridge University Press must be obtained prior to any commercial use.
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