Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An incompleteness theorem via ordinal analysis   We present an analogue of G\"{o}del's second incompleteness theorem for
systems of second-order arithmetic. Whereas G\"{o}del showed that sufficiently
strong theories that are $\Pi^0_1$-sound and $\Sigma^0_1$-definable do not
prove their own $\Pi^0_1$-soundness, we prove that sufficiently strong theories
that are $\Pi^1_1$-sound and $\Sigma^1_1$-definable do not prove their own
$\Pi^1_1$-soundness. Our proof does not involve the construction of a
self-referential sentence but rather relies on ordinal analysis.

26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys