6 problems

Let $\mathsf{WSeq}$ be the weak sequence theory and let $\mathsf{R}$ be Robinson's arithmetic. Mutual interpretability conjecture. The theories $\mathsf{WSeq}$ and $\mathsf{R}$ are…

Let $\mathsf{T}$ be the tree theory and let $\mathsf{Q}$ be Robinson arithmetic. Kristiansen–Murvanashyaka conjecture. The theory $\mathsf{Q}$ interprets $\mathsf{T}$. They prove t…

The paper considers the $1$-finite variational principle ($1$-$\mathrm{FVP}$) and the finite variational principle ($\mathrm{FVP}$) for a space $\mathcal{X}$, formalized over the w…

Conjectured falsity of $\mathrm{PH}{\downarrow}$. The statement $\mathrm{PH}{\downarrow}$ is conjectured to be false. The paper describes this as the best known complexity-theoreti…

Relativized consistency-and-provability conjecture. There exists such a theory $T(\alpha)$ for which

KMM–PHP equivalence conjecture. The first assertion, $\mathbf{LA}\cup\mathrm{KMM}\vdash\mathrm{PHP}$, is true. The paper states that this implication should not be too difficult to…