Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Possible pcf algebras   There exists a family $\{B_{\alpha}\}_{\alpha<\omega_1}$ of sets of countable
ordinals such that
  o $\max B_{\alpha}=\alpha$,
  o if $\alpha\in B_{\beta}$ then $B_{\alpha}\subseteq B_{\beta}$,
  o if $\lambda\leq \alpha$ and $\lambda$ is a limit ordinal then
$B_{\alpha}\cap\lambda$ is not in the ideal generated by the $B_{\beta}$,
$\beta<\alpha$, and by the bounded subsets of $\lambda$,
  o there is a partition $\{A_n\}_{n=0}^{\infty}$ of $\omega_1$ such that for
every $\alpha$ and every $n,$ $B_{\alpha}\cap A_n$ is finite.

19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg