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We prove a definable version of Matou\v{s}ek's $(p,q)$-theorem in NIPtheories. This answers a question of Chernikov and Simon. We also prove auniform version.  The proof builds on a proof of Boxall and Kestner who proved this theorem inthe distal case, utilizing the notion of locally compressible types whichappeared in the work of the author with Bays and Simon.

A definable $(p,q)$-theorem for NIP theories