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.
|Journal of the Institute of Mathematics of Jussieu
|Accepted/In press - 2023
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© The Author(s), 2023. Published by Cambridge University Press.
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