ON LARGE EXTERNALLY DEFINABLE SETS IN NIP

Martin Bays, Omer Ben-Neria, Itay Kaplan, Pierre Simon

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
JournalJournal of the Institute of Mathematics of Jussieu
DOIs
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.

Keywords

  • 03C45
  • 03C55
  • 2020 Mathematics subject classification

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