4 problems

A field is called stable if its first-order theory is stable, simple if its theory is simple, separably closed if it has no proper finite separable algebraic extension, and pseudo-…

Large-simple-field PAC conjecture. Every large simple field is $\mathrm{PAC}$.

Let $K$ be an infinite (super)-simple field. The simple fields conjecture. $K$ is a (perfect) PAC field. Duret showed that this conjecture implies the stable fields conjecture, but…

Finite generation conjecture. If $M$ is PAC over $K$, then