T is a simple first order theory as defined by Shelah. $M$ is a model of $T$. I write $acl^n(A)$ for the set of elements in $M$ lying in a finite $A$-definable set of size at most $n$. If $a$ and $b$ are independant, does the following equality hold? $$acl^n(a)\cap acl^n(b)=acl^n(\emptyset)$$

EDIT : I don't know why, but I expect this to be false, so let me ask : is there a constant $k$ (depending on T and $n$) such that for all independent $a$ and $b$ over $0$, one would have

$$acl^n(a)\cap acl^n(b)\subset acl^{k.n}(\emptyset)$$