A stationary type in a stable theory is said to be **regular** if it is orthogonal to all its forking extensions. If , this means that whenever and and is stationary, then and are orthogonal. Regularity is a parallelism invariant: if is a forking extension of , then is regular if and only if is regular.

Types of U-rank 1 are regular, because their non-forking types are algebraic, hence orthogonal to every type. More generally, any type whose U-rank is a power is regular.

*Proof.* This comes from the fact that if and are types of rank and rank , then and are orthogonal. Indeed, if and , then by the Lascar inequalities, . Since is less than , this forces . Then , so . QED

In DCF, the generic type of the home sort (which has rank ) and the generic type of the constant field (which has rank 1) are two examples of regular types.

If is a regular type over a set , there is a natural pregeometry structure on the set of realizations of . A set is independent if and only if it is independent in the sense of stability theory, i.e., , , and so on. If is a set of realizations of , a tuple is in the closure of if and only if .

Regular types have weight 1.

Regular types are prevalent in superstable theories, in some sense… ::: ::: :::