Abstract
We prove a definable version of Matoušek's (p,q)-theorem in NIP theories. This answers a question of Chernikov and Simon. We also prove a uniform version. The proof builds on a proof of Boxall and Kestner who proved this theorem in the distal case. It utilizes the notion of locally compressible types which appeared in the work of the author with Bays and Simon.
Original language | English |
---|---|
Article number | 109418 |
Journal | Advances in Mathematics |
Volume | 436 |
DOIs | |
State | Published - Jan 2024 |
Keywords
- (p,q) theorem
- Forking
- Model theory
- NIP
All Science Journal Classification (ASJC) codes
- General Mathematics