2 problems

Invariant-type quotient conjecture. There are $b\in\mathcal U$ and a formula $\psi(z;y)$ such that $\operatorname{tp}(b/N)$ is finitely satisfiable in $M$ and

Extensible definability conjecture. There is $\theta(y)\in \operatorname{tp}(d/M)$ such that the partial type