5 problems

The maximality conjecture. The relation \mathrel{\raise0.2ex\text{\ooalign{\hidewidthvert\hidewidth\cr\raise-0.9ex\text{smile}}}}^{nm} is the maximum strongly admissible geom…

Let $(X,T)$ be a distal minimal topological dynamical system, and let ${\bf Ind}^{[d]}_{ap}(X,T)$ denote its arithmetic-progression independence relation of order $d$. Let…

Let $T$ be a simple theory, and let $\thind$ denote thorn-independence in $T$. Canonicity conjecture. In any simple theory, $\thind$ is canonical. This conjecture proposes that tho…

Extension conjecture for lovely pairs. There exists an independence relation mathop{\mathpalette\Ind{}^{\!\!\!\!\rlap{scriptscriptstyletextnormal{2}}\,\,\,\,}} on…

Finitarity and definability conjecture. $\operatorname{cl}$ is always finitary. Moreover, $\operatorname{cl}$ is definable: for every small $A\subseteq\mathfrak C$, the set…