3 problems

Axiomatization conjecture. The axioms and schemata $(1)$–$(17)$ axiomatize $_2$.

Sound reflection hierarchy classification conjecture. For every $n\in\mathbb{N}$, both of the following hold: (1) there exists a $0^{(n)}$-recursive sequence $(T_n)_{n<\omega}$ of…

Monotone-operator classification conjecture. For some $\beta\preceq\alpha$ and some true sentence $\varphi$, for every $\psi$ such that $T+\psi\vdash\varphi$,