Submission date: 24 May 2022

Abstract:

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

Keywords and phrases:

Full text arXiv 2205.11792: pdf, ps.