Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PCF theory: applications   We deal with several pcf problems; we characterize another version of
exponentiation: number of kappa-branches in a tree with lambda nodes, deal with
existence of independent sets in stable theories, possible cardinality of
ultraproduct, the depth of ultraproducts of Boolean Algebras. Also we give
cardinal invariant for each lambda with pcf restriction and investigate further
T_D(f) .

17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg