Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ultrafilters on $G$-spaces   For a discrete group $G$ and a discrete $G$-space $X$, we identify the
Stone-\v{C}ech compactifications $\beta G$ and $\beta X$ with the sets of all
ultrafilters on $G$ and $X$, and apply the natural action of $\beta G$ on
$\beta X$ to characterize large, thick, thin, sparse and scattered subsets of
$X$. We use $G$-invariant partitions and colorings to define $G$-selective and
$G$-Ramsey ultrafilters on $X$. We show that, in contrast to the
set-theoretical case, these two classes of ultrafilters are distinct. We
consider also universally thin ultrafilters on $\omega$, the $T$-points, and
study interrelations between these ultrafilters and some classical ultrafilters
on $\omega$.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
1
The categories of this paper are: cs