It is well known that not every map $f:\mathbb{Z}_{p^k}\to\mathbb{Z}_{p^k}$, $p$ prime, is induced by a polynomial of $\mathbb{Z}_{p^k}[x]$. What about rational maps $p(x)/q(x)$? I …

Is there an oracle such that in the relativized world, bd-Frege (bounded depth Frege propositional proof system) has FIP (feasible interpolation property) but Frege does not hav …