5 problems

Let $\operatorname{\mathcal{K}}$ be an abstract elementary class. If $\operatorname{\mathcal{K}}$ is $\chi$-tame for some cardinal $\chi$, then there exists a cardinal…

Unknown implication conjecture. The unknown implications displayed in the figure also hold true.

Let $\mathbf{K}$ be an abstract elementary class, let $\lambda$ be a cardinal, and suppose that $\mathbf{K}$ has amalgamation in cardinality $\lambda^+$. A good $\lambda$-frame is…

Grossberg–VanDieren's categoricity-to-tameness conjecture. Suppose $K$ is an AEC. If $K$ is categorical in some $\lambda \geq Hanf(LS(K))$ (or some other value depending only on…

Let $G$ be a finitely generated nilpotent-by-abelian group. Let $N$ be a nilpotent normal subgroup with $Q=G/N$ abelian, and consider the factors of the lower central series of $N$…