Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure in sets with logarithmic doubling   Suppose that G is an abelian group, A is a finite subset of G with |A+A|<
K|A| and eta in (0,1] is a parameter. Our main result is that there is a set L
such that |A cap Span(L)| > K^{-O_eta(1)}|A| and |L| = O(K^eta log |A|). We
include an application of this result to a generalisation of the Roth-Meshulam
theorem due to Liu and Spencer.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int