Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short Proofs for Slow Consistency   Let $\operatorname{Con}(\mathbf T)\!\restriction\!x$ denote the finite
consistency statement "there are no proofs of contradiction in $\mathbf T$ with
$\leq x$ symbols". For a large class of natural theories $\mathbf T$, Pudl\'ak
has shown that the lengths of the shortest proofs of
$\operatorname{Con}(\mathbf T)\!\restriction\!n$ in the theory $\mathbf T$
itself are bounded by a polynomial in $n$. At the same time he conjectures that
$\mathbf T$ does not have polynomial proofs of the finite consistency
statements $\operatorname{Con}(\mathbf T+\operatorname{Con}(\mathbf
T))\!\restriction\!n$. In contrast we show that Peano arithmetic
($\mathbf{PA}$) has polynomial proofs of
$\operatorname{Con}(\mathbf{PA}+\operatorname{Con}^*(\mathbf{PA}))\!\restriction\!n$,
where $\operatorname{Con}^*(\mathbf{PA})$ is the slow consistency statement for
Peano arithmetic, introduced by S.-D. Friedman, Rathjen and Weiermann. We also
obtain a new proof of the result that the usual consistency statement
$\operatorname{Con}(\mathbf{PA})$ is equivalent to $\varepsilon_0$ iterations
of slow consistency. Our argument is proof-theoretic, while previous
investigations of slow consistency relied on non-standard models of arithmetic.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
29
The categories of this paper are: funct-an