11 problems

Turing's conjecture. For every arithmetical theorem $\varphi$, there is a computable presentation of an ordinal $\alpha$ such that

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

Weakest-extensional-operator conjecture. The consistency operator is the weakest extensional operator that is stronger than the identity operator.

Consistency-operator canonicity conjecture. The consistency operator and its iterates are canonical among recursive extensional functions.

A reflection principle is a schema of set-theoretic sentences expressing reflection from the universe to some initial segment $V_\alpha$. Let $\kappa(\omega)$ denote the first…

Koellner's conjecture. Intrinsic justifications do not take us to the point of an $\omega$-Erdős cardinal.

Let ${\mathop{\rm Refl}}_{\mathop{\rm wc}}(\kappa)$ denote the weakly compact reflection principle at a cardinal $\kappa$. A cardinal $\kappa$ is a weak compactness reflection card…

Let $\textup{MM}(S)[S]$ denote the stated forcing axiom, and let SRP (the Strong Reflection Principle) be the principle asserting that whenever $[?]$ [the principle is defined in t…

Let $L$ be a number field with Galois group $S_4$ or $A_4$ over $\mathbb{Q}$. Let $K_1$ be a quartic subfield and $K_2$ its cubic resolvent. For a number field $K$, write…

Let $\mathcal T$ be the class of theories under consideration, and let $\Sigma^b_1RFN_T(\bar n)$ denote the finite $\Sigma^b_1$ reflection principle for $T$. Nonuniform reflection…

Let $\mathsf{BSRP^{s}}(\omega_2)$ denote the bounded strong reflection principle at $\omega_2$. An inner model with a Woodin cardinal is a model of the relevant set-theoretic theor…