Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial properties of non-archimedean convex sets   We study combinatorial properties of convex sets over arbitrary valued
fields. We demonstrate analogs of some classical results for convex sets over
the reals (e.g. the fractional Helly theorem and B\'ar\'any's theorem on points
in many simplices), along with some additional properties not satisfied by
convex sets over the reals, including finite breadth and VC-dimension. These
results are deduced from a simple combinatorial description of modules over the
valuation ring in a spherically complete valued field.

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The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex