Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Ramsey for $\mathcal{R}_{1}$ ultrafilter mappings and their Dedekind
  cuts
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex