8 problems

Stable forking conjecture. In a simple theory $T$, forking is explained by the stable part of $T$.

Let $T$ be a stable theory, let $M$ be a model of $T$, and let $A\subseteq M$ be arbitrary. The set $A$ is weakly benign in $M$ if equality of strong types over $A$ implies equalit…

Let $T$ be a stable theory, let $M$ be a model of $T$, and let $A\subseteq M$. The set $A$ is benign in $M$ if equality of types over $A$ implies equality of the corresponding type…

Kikyo–Pillay's conjecture. If $T_\sigma$ has a model companion, then $T$ has the definable multiplicity property.

Stable shift-graph embedding conjecture. If, for every cardinal $\mu$,

Equivalence conjecture. The following are equivalent: $T$ is bounded; $T$ is dimensional; and $\mathfrak e$ is surjective.

Stability conjecture for strongly $2$-dependent groups. Every strongly $2$-dependent group is stable; equivalently, if $G$ is a group such that

Canonical base property conjecture. Every finite-rank stable theory has the canonical base property.