Fields and Fusions: Hrushovski constructions and their definable groups

An overview is given of the various expansions of fields and fusions of strongly minimal sets obtained by means of Hrushovski's amalgamation method, as well as a characterization of the groups definable in these structures

Interpreting structures of finite Morley Rank in strongly minimal sets

We 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.</p