3 problems

Let $\mathcal S$ be the base arithmetic theory under consideration, and let $Con_{\mathcal S}(n)$ denote its bounded consistency statement at length $n$. Write…

Polynomial consistency-speedup conjecture. For every sound $\Delta^b_1(S^1_2)$ theory $S$ and every $l\in\omega$, there exists a sound $\Delta^b_1(S^1_2)$ theory $T$ such that

Classification conjecture for monotone proof-theoretic operators. Suppose $\mathfrak{g}$ is monotone, non-constant, and recursive, with $\mathfrak{g}(\varphi)\in\Pi_1$ for every se…