A theory $T$ with home sort $M$ is said to be dp-minimal if it satisfies one of the following equivalent conditions:

Whenever $I$ and $I'$ are two mutually indiscernible sequences and $a$ is a singleton from the home sort, one of $I$ or $I'$ is indiscernible over $a$ .
Whenever $\langle b_{i}\rangle _{i\in I}$ is an indiscernible sequence and $a$ is a singleton from the home sort, there is some $i_{0}\in I$ such that $\langle b_{i}\rangle _{i>i_{0}}$ and $\langle b_{i}\rangle _{i<i_{0}}$ are $a$ -indiscernible.
The home sort has dp-rank 1.
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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. ::: ::: :::