Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof theory for theories of ordinals III: $\Pi_{N}$-reflection   This paper deals with a proof theory for a theory of $\Pi_{N}$-reflecting
ordinals using a system of ordinal diagrams. This is a sequel to the previous
one(APAL 129)in which a theory for $\Pi_{3}$-reflection is analysed
proof-theoretically.

6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga