The directed-family IP conjecture for expansions of infinite fields

Let ${\mathscr{F}}$ be an expansion of an infinite field $F$. A family ${\mathcal X}$ of subsets of $F$ is directed when any two members have a common member containing their union. Directed-family IP conjecture. If ${\mathscr{F}}$ admits a definable directed family ${\mathcal X}$ of finite subsets of $F$ such that $\bigcup {\mathcal X}=F$, then ${\mathscr{F}}$ has the independence property. This generalizes the natural-number conjecture and is intended to rule out NIP expansions of fields covered by such a definable exhaustion.