Hrushovski-Fraïssé Structures

Hrushovski constructed many examples of (seemingly) exotic strongly minimal structures as direct limits of certain classes of finite structures defined by simple combinatorial dimension functions.

These structures violate Zilber's conjecture on both counts: there are examples of non-locally modular Hrushovski-Fraïssé limits which do not interpret a group, much less a field. Moreover, there are examples of such structures which carry two different field structures. These cannot be interpreted in any field.