Let $T$ be totally transcendental theory. (stable in particular)
I want to prove that $a\overset{\vert}{\smile}_{A}b$ iff $MR(a/A)=MR(a/Ab)$
Well we know that since $T$ is totally transcendental then every formula and in prticular every type has a Morely Rank. So we can talk about the problem.
And $T$ is stable so forking and dividing coincide.
By that i managed to prove the "$\Leftarrow$" direction, by showing that if $tp(a/Ab)$ forks over $A$ then $MR(a/A)>MR(a/Ab)$.
But i can't manage to prove the second direction. I though maybe to assume that $MR(a/A)>MR(a/Ab)$ and take $\varphi \in tp(a/A)$ and $\psi \in tp(a/Ab)$ s.t $\psi(\mathfrak C)\subseteq\varphi(\mathfrak C)$ ($\mathfrak C$ is the monster) with $MR\psi<MR\varphi$. Than to find some how a way to show that $\psi$ divides.