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arXiv · 2205.11792

On large externally definable sets in NIP

Martin Bays·Omer Ben-Neria·Itay Kaplan·Pierre Simon
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Abstract

We study cofinal systems of finite subsets of $\omega_1$. 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.

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Martin Bays, Omer Ben-Neria, Itay Kaplan, Pierre Simon. 2022-05-24. On large externally definable sets in NIP. https://doi.org/10.1017/s1474748023000464

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