In a stable theory every global type $p$ is invariant (= non-forking) over ${\rm acl^{eq}}(A)$ for some set $A$. Is there a characterization of superstability and/or $\omega$-stability in terms of the minimal size of such $A$?
Sorry for the nebulous question, I vaguely remember reading something of this sort.
A global type $p$ doesn't fork over $A$ iff it is definable (iff it is invariant) over $acl^{eq}(A)$. Now a stable theory is superstable iff every type does not fork over a finite set. Hence a stable theory is superstable iff every global type is definable (invariant) over $acl^{eq}(A)$ for some finite $A$.