Work in a stable theory (or more generally a simple theory) . The preweight of a complete type is defined to be the supremum of the cardinals such that there is some -independent set such that forks with for every , i.e., for every . This is well-defined, and in fact the preweight of is bounded above by the appearing in the local character of forking (which is for superstable theories).
If is a stationary type, the weight of is defined to be the largest weight of any non-forking extension of . Types of Morley rank 1, or more generally, Lascar rank 1 have weight 1. More generally, regular types have weight 1.
Weight is generalized to simple theories in a straightforward way. Weight is generalized to NIP theories by the notion of dp-rank, and is generalized to NTP2 theories by the notion of burden.
Superstable theories have plenty of weight 1 types, in some sense… (Every type is domination equivalent to a product of weight 1 type. Also, every type has finite weight.) ::: ::: :::