The definable (p,q) theorem for NIP theories
Abstract
I will discuss the following statement, a definable version of the (p,q) theorem of Jiří Matoušek from combinatorics, conjectured by Chernikov and Simon:
Suppose that T is NIP and that phi(x,b) does not fork over a model M. Then there is some formula psi(y) in tp(b/M) such that the partial type {phi(x,b’) : psi(b’)} is consistent.