# On uniform definability of types over finite sets for NIP formulas

## TL;DR

This paper proves that a formula is NIP if and only if it satisfies uniform definability of types over finite sets, settling a conjecture and linking model theory with machine learning concepts.

## Contribution

It establishes the equivalence between NIP and UDTFS for formulas, confirming a conjecture and advancing understanding of model-theoretic properties.

## Key findings

- Proves NIP iff UDTFS for formulas
- Settles Laskowski's conjecture
- Links model theory with machine learning theory

## Abstract

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.