Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The higher sharp I: on $M_1^\#$   We establish the descriptive set theoretic representation of the mouse
$M_n^{\#}$, which is called $0^{(n+1)\#}$. This part deals with the case $n=1$.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th