Interpreting structures of finite Morley Rank in strongly minimal sets

AbstractWe show that any structure of finite Morley Rank having the definable multiplicity property (DMP) has a rank and multiplicity preserving interpretation in a strongly minimal set. In particular, every totally categorical theory admits such an interpretation. We also show that a slightly weaker version of the DMP is necessary for a structure of finite rank to have a strongly minimal expansion. We conclude by constructing an almost strongly minimal set which does not have the DMP in any rank preserving expansion, and ask whether this structure is interpretable in a strongly minimal set