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Preprint Number 2188

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2188. Martin Bays, Omer Ben-Neria, Itay Kaplan, Pierre Simon
On large externally definable sets in NIP

Submission date: 24 May 2022


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.

Mathematics Subject Classification: 03C45

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Full text arXiv 2205.11792: pdf, ps.

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