7 problems

Martin's conjecture. Assume $AD$. Then:

For $p\in\mathbb{N}^{\mathbb{N}}$, let $\mathsf{TDINC}(p)$ consist of sequences $\langle p_0,p_1,p_2,\ldots\rangle$ such that, for every $i$,…

Let $\mathsf{NON}$ be the problem discussed in the paper, and let $\mathsf{NON}^\omega$ and $\mathsf{NON}^\infty$ denote its countable and inverse-limit iterations, respectively. T…

C.e. Sigma-intermediate/Delta-low conjecture. There is a computably enumerable set that is intermediate for $\Sigma$-Feiner and low for $\Delta$-Feiner.

Let $e\in\mathbb{N}$ and let $A$ be a real such that … For a real $B$, define the $e$-th pseudo-hyperjump by $\operatorname{HJ}_e(B)=B\oplus V_e^B$, where $V_e^B$ is the $e$-th mem…

Lowness conjecture. Under these assumptions, $[\mathbf a,\mathbf g]$ is $\Sigma^0_1(\mathbf x)$-presentable.

Let $A$ be a set of natural numbers, let $A'$ denote its Turing jump, and let $0”$ denote the second Turing jump of the computable degree. A set is almost everywhere dominating whe…