Recall that a strongly minimal theory $T$ has the Definable Multiplicity Property (DMP) if for all natural $k$, $m$ and $\varphi(\bar{x},\bar{b})$ of rank $k$, multiplicity $m$, there exists a formula $\theta ∈ tp(\bar{b})$ such that for all $\bar{b^{'}}\models\theta$, $rk(\varphi(\bar{x},\bar{b^{'}}))=k$ and $mult(ϕ(\bar{x},\bar{b^{'}})) = m$.


**Question.** Does every strongly minimal set have a strongly minimal
expansion with DMP?


(Any reference will be appreciated.)



Strongly minimal set with DMP
The answer is no, there is a counter example by Hasson and Hrushovski, constructed using Fraisse limit. It is described in their article "DMP in strongly minimal sets", J. Symbolic Logic
Volume 72, Issue 3 (2007), 1019-1030.


