Title: Short Proofs for Slow Consistency,
Abstract: 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 $\mathbf T$, Pudlák
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.