Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superfilters, Ramsey theory, and van der Waerden's Theorem   Superfilters are generalized ultrafilters, which capture the underlying
concept in Ramsey theoretic theorems such as van der Waerden's Theorem. We
establish several properties of superfilters, which generalize both Ramsey's
Theorem and its variant for ultrafilters on the natural numbers. We use them to
confirm a conjecture of Ko\v{c}inac and Di Maio, which is a generalization of a
Ramsey theoretic result of Scheepers, concerning selections from open covers.
Following Bergelson and Hindman's 1989 Theorem, we present a new simultaneous
generalization of the theorems of Ramsey, van der Waerden, Schur,
Folkman-Rado-Sanders, Rado, and others, where the colored sets can be much
smaller than the full set of natural numbers.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs