Title: NIP formulas and Baire 1 definability,
Abstract: In this short note, using results of Bourgain, Fremlin, and Talagrand
\cite{BFT}, we show that for a countable structure $M$, a saturated elementary
extension $M^*$ of $M$ and a formula $\phi(x,y)$ the following are equivalent:
(i) $\phi(x,y)$ is NIP on $M$ (in the sense of Definition 2.1).
(ii) Whenever $p(x)\in S_\phi(M^*)$ is finitely satisfiable in $M$ then it is
Baire 1 definable over $M$ (in sense of Definition 2.5).