Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounding 2D Functions by Products of 1D Functions   Given sets $X,Y$ and a regular cardinal $\mu$, let $\Phi(X,Y,\mu)$ be the
statement that for any function $f : X \times Y \to \mu$, there are functions
$g_1 : X \to \mu$ and $g_2 : Y \to \mu$ such that for all $(x,y) \in X \times
Y$, $$f(x,y) \le \max \{ g_1(x), g_2(y) \}.$$ In ZFC, the statement
$\Phi(\omega_1, \omega_1, \omega)$ is false. However, we show the theory ZF +
"the club filter on $\omega_1$ is normal" + $\Phi(\omega_1, \omega_1, \omega)$
(which is implied by ZF + DC + "$V = L(\mathbb{R})$" + "$\omega_1$ is
measurable") implies that for every $\alpha < \omega_1$ there is a $\kappa \in
(\alpha,\omega_1)$ such that in some inner model, $\kappa$ is measurable with
Mitchell order $\ge \alpha$.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio