Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Externally definable sets and dependent pairs   We prove that externally definable sets in first order NIP theories have
honest definitions, giving a new proof of Shelah's expansion theorem. Also we
discuss a weak notion of stable embeddedness true in this context. Those
results are then used to prove a general theorem on dependent pairs, which in
particular answers a question of Baldwin and Benedikt on naming an
indiscernible sequence.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin