13 problems

Let the logic of Section $\mathrm{logics}$ be the logic studied in the paper, and let its completeness proof be the proof given in the appendix. Consider more expressive languages…

Expanding commutator conjecture. Setting $\mathsf{L}_v\in\{\mathsf{K4},\mathsf{K4.3}\}$ should lead to incompleteness, whereas setting…

Let $\mathsf{DDNS}_{\mathcal{C}}$ denote the disjunctive double-negation scheme for the class $\mathcal{C}$, and let $\mathsf{DNS}^{\forall}_{\mathcal{C}}$ denote the corresponding…

Let $L$ be a modal logic, and let a descriptive frame and a Kripke frame for $L$ have their usual meanings. Say that $L$ is strongly Kripke complete when every $L$-consistent set o…

Let $\mathbb{R^{Z_<}}$ be the set equipped with the $\mathfrak{e}$-topology, and call a sequence in $\mathbb{R^{Z_<}}$ hyper-Cauchy when for every $\mathfrak{e}\in\mathbb{R^{Z_<}}$…

Let ${\bf K^W}$ be the logic considered in the paper, let a filter be a neighborhood frame whose neighborhood collections satisfy the filter conditions defined in the surrounding d…

Coprime-order completeness conjecture. Then $m$ is complete.

Completeness conjecture for two-dimensional cell complexes. The logic $\mathbf{DT_1C}+Ku_2$ is complete with respect to two-dimensional cell complexes, more exactly, adjunction spa…

Let $n>2$, let $\mathbf{X}=G=\mathrm{PO}(n,1)$, and let $\mathbf{G}=G\times G$ act on $\mathbf{X}$ by left and right multiplication. For a compact manifold $N$, a…

Let $X$ have density … where $c>0$ is known and the parameter space is $\mathbb{R}\setminus\{0\}$. Pinelis's completeness conjecture. The statistic $X$ is complete. For the paramet…

Let $G$ be a metric group, let $A=(a_n)$ be an AP sequence in $G$, and let $H$ be the smallest closed subgroup of $G$ containing $A$. AP-sequence completeness or infinite-product c…

Let $M$ be a compact complex manifold endowed with a holomorphic Riemannian metric of constant non-vanishing curvature. The dimension of $M$ is the complex dimension. Dumitrescu–Ze…

Let $M$ be an $n$-dimensional manifold with a coframing, and let its canonical metric be the Riemannian metric induced by the coframing. Consider the Lie algebra of vector fields g…