Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Usuba's principle $UB_\lambda$ can fail at singular cardinals   We answer a question of Usuba by showing that the combinatorial principle
$UB_\lambda$ can fail at a singular cardinal. Furthermore, $\lambda$ can be
taken to be $\aleph_\omega.$

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph