Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets (UDTFS). This settles a conjecture of Laskowski.
Bibliographical noteFunding Information:
I. Kaplan would like to thank the Israel Science Foundation for partial support of this research (Grants Nos. 1533/14 and 1254/18). We thank the anonymous referee for their remarks, and specifically for suggesting to add Remark 12 which certainly helps the presentation.
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- Local UDTFS
- local NIP
- recursive teaching dimension
- sample compression schemes