Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Can groupwise density be much bigger than the non-dominating number?   We prove that g (the groupwise density number) is smaller or equal to b^+
(the successor of the minimal cardinality of a non-dominated subset of
omega^omega).

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph