Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of ordinal analysis   Ordinal analysis induces a partition of $\Sigma^1_1$-definable and
$\Pi^1_1$-sound theories whereby two theories are equivalent if they have the
same proof-theoretic ordinal. We show that no equivalence relation $\equiv$ is
finer than the ordinal analysis partition if both: (1) $T\equiv U$ whenever $T$
and $U$ prove the same $\Pi^1_1$ sentences; (2) $T\equiv T+U$ for every set $U$
of true $\Sigma^1_1$ sentences. In fact, no such equivalence relation makes a
single distinction that the ordinal analysis partition does not make.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int