Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A direct proof of the five element basis theorem   We present a direct proof of the consistency of the existence of a five
element basis for the uncountable linear orders. Our argument is based on the
approach of notion of saturation of Aronszajn trees considered by Koenig,
Larson, Moore and Velickovic and simplifies the original proof of Moore.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int