Fix some theory . Let be a cardinal. An ict pattern of depth is a collection of formulas and constants for and , such that for every , the following collection of formulas is consistent: So we have an array of formulas, with rows and columns, each row being uniform, and for every vertical path through the array, there is an element which satisfies exactly those formulas along the path, and no others.

More generally, if is a partial type over some parameters, then an ict pattern of depth in is an array as above, such that for each , is consistent.

Given an ict pattern, we can always extract another ict pattern using the same formulas, but with the mutually indiscernible.

Shelah defines of the theory to be the supremum of the depths of ict patterns, or if there exist ict patterns of unbounded depth. It turns out that if and only if is NIP.

A theory is said to be strongly dependent if there are no ict patterns of depth . The maximum depth of an ict pattern in a type is the dp-rank of , or some variant thereof. ::: ::: :::