Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of the Erd\"os similarity conjecture   We show that for any infinite set $A$ in ${\mathbb R}$, there exists a
compact set $E \subseteq \mathbb{R}$ of positive Lebesgue measure that does not
contain any non-trivial affine copy of $A$. This proves the Erd\"os similarity
conjecture.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat