5 problems

Analytic-choice conjecture. The degree lies strictly above every $\lim^{(n)}$; hence $\mathrm{SCI}_{\mathrm{TTE}}=\infty$, and it may coincide with a known “analytic choice” princi…

Let $\mathcal{C} = \mathsf{Mod}(\mathcal{K}_2^{\mathrm{rec}},\mathcal{K}_2)$, and let $P$ and $Q$ be objects of $\mathsf{Cont}(p\mathcal{C})$. The sequential products $P \star Q$ a…

Let $\mathsf{COH}$ denote the cohesive principle, let $\operatorname{\mathsf{Ind}}\mathscr{E}_k$ denote the indicated indivisibility problem for $k$-colorings, and let…

Let $(X,\delta)$ be a represented space, let ${\rm C}_X$ denote closed choice on $X$, and let $\lim$ denote the limit operation on Baire-space names. Non-characterization conjectur…

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…