12 problems

Let $V$ be a model of $\mathsf{ZF}+\mathsf{KWP}$, let $G$ be a $V$-generic filter, and let $W$ be an intermediate model of $\mathsf{ZF}$ with … Here, $\mathsf{KWP}$ means that ever…

Weak FAFA equivalence conjecture. The principles

Negative-answer conjecture. The question should have a negative answer: there should be a symmetric extension $N$ satisfying $\mathrm{BPI}$ for which no symmetric system presenting…

Truss's conjecture. For every amorphous set $A$, $\operatorname{fin}(A)$ is dually Dedekind finite.

Finite-$\Sigma^1_1$-choice non-derivability conjecture. The principle \textup{\textsf{finite-}\Sigma^1_1\text{-AC}_0} cannot be obtained from item (ii).

Finite Choice non-derivability conjecture. The principle $\textup{\textsf{Finite Choice}}$ cannot be obtained from the second item.

Let $\mathbf{M}(C,S)$ be the statement under consideration, and let $\mathcal{N}_{\mathbf{2}^{\omega}}$ denote the model of set theory constructed from $\mathbf{2}^{\omega}$. The c…

Let $\text{\rm\sffamily CC}_2$ denote connected choice for non-empty connected closed subsets of $[0,1]^2$. For a multi-valued operation $f$, write $\operatorname{id}\times f$ for…

Let $\text{\rm\sffamily CC}_2$ denote connected choice for non-empty connected closed subsets of $[0,1]^2$. For a multi-valued operation $f$, write $f\times f$ for two parallel ins…

Let $\text{\rm\sffamily CC}_2$ be connected choice for non-empty connected closed subsets of $[0,1]^2$, and let $\text{\rm\sffamily C}_{[0,1]}$ be closed choice on the unit interva…

Let $\text{\rm\sffamily CC}_n$ denote connected choice for subsets of $[0,1]^n$, and let $\text{\rm\sffamily C}_{[0,1]}$ denote closed choice on the unit interval. Weihrauch reduci…

Let ${\rm UC}_X$ denote the unique closed choice operation on a represented Hausdorff space $X$, and let ${\rm C}_X$ denote closed choice on $X$. For Baire space…