8 problems

Chang–Morel's conjecture. Every elementary class closed under reduced products is a Horn class.

Continuous-model-theory analogue conjecture. Results analogous to the main theorems of the paper should hold in continuous model theory.

Optimality conjecture. The assumptions on the ideal $$ in this theorem are far from optimal.

OCA$_T$ rigidity conjecture. $\operatorname{{\mathsf {OCA}_T}}$ alone suffices for all rigidity results for quotients of reduced products of countable structures modulo analytic id…

OCA$_T$ conjecture. The conclusion of Proposition $$ follows from $\operatorname{{\mathsf {OCA}_T}}$ alone.

Forcing obstruction conjecture. The poset $\mathbb{E}_A$ forces that $A$ does not embed into $\ell_\infty/c_0$.

Atomic saturation conjecture.

Reduced-power maximality conjecture. $(T,\Delta)$ is $\trianglelefteq_{{\rm rp}}$-maximal if and only if $(T,\Delta)$ has the ${\rm SOP}_3$.