7 problems

Nonrepresentability conjecture. Some natural degrees, such as $\mathsf{RT}^2_2$, are not equivalent to any \mathsf{Ans}(\left\llangle E \right\rrangle).

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 $n$ and $m$ be the parameters for the corresponding Borel measurability levels, and let $\mathbf{X}$ and $\mathbf{Y}$ be Polish represented spaces. Write $\mathfrak{b}$ for the…

Let $n$ and $m$ be the parameters for the corresponding Borel measurability levels, and let $\boldsymbol{X}$ and $\boldsymbol{Y}$ be Polish represented spaces. Write $\mathfrak{b}$…

Brattka–Miller's conjecture. Dimension should be the crucial demarcation line for spaces with only Turing degrees.

Let $\beta$ and $\alpha$ be ordinals with $\beta < \alpha$, and let $\mathbf{X}$ be a represented space. Write $\mathbf{X}^{(\alpha)}$ for its $\alpha$-th jump and $\chi^{(\beta)}$…

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…