Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: NIP formulas and Baire 1 definability   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).

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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph