A theory T with home sort M is said to be dp-minimal if it satisfies one of the following equivalent conditions:
TODO: check that these definitions are correct.
If a theory is dp-minimal, it is NIP, and in fact strongly dependent. Strongly-minimal, o-minimal, C-minimal, and p-minimal theories are all dp-minimal, as are theories of VC-density 1. (TODO: check these claims.)
There is more generally a notion of dp-rank, and a set is dp-minimal if and only if it has dp-rank 1.
Expanding the theory by naming constants preserves dp-minimality. ::: ::: :::