Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covering of ordinals   The paper focuses on the structure of fundamental sequences of ordinals
smaller than $\epsilon_0$. A first result is the construction of a monadic
second-order formula identifying a given structure, whereas such a formula
cannot exist for ordinals themselves. The structures are precisely classified
in the pushdown hierarchy. Ordinals are also located in the hierarchy, and a
direct presentation is given.

24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess