Regular types

In a stable theory, we say that the type p is regular if every forking extension is orthogonal to p. Equivalently, a type p ∈ S(B) is regular if the operation clp(A) := {a ∈ p(M) | tp(a/AB) forks over B} defines a pregeomety on the set of realizations of p in a very saturated model M.

Minimal types are regular, but in general superstable theories, one must also consider regular types of transfinite rank in order to analyze general types.