5 problems

Stable forking conjecture over a base. If $a \mathrel{\mathop{\mathpalette\notind{}}_{C}} b$, there is a formula $\varphi(x,b)\in\operatorname{tp}(a/Cb)$ which forks over $C$, such…

Stable forking conjecture. If $a \mathrel{\mathop{\mathpalette\notind{}}_{C}} b$, then there is a formula $\varphi(x,\overline{b})\in\operatorname{tp}(a/Cb)$ such that…

Kim's pseudolinearity conjecture. If $\mathrm{SU}(p)=1$ and $p$ is $k$-linear for some $k<\omega$, then $p$ is linear.

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…

Independence characterization conjecture. Then