Forking Independence

A ternary relation between parameter sets A, B over a base C in model theory (typically stable or simple theories) that expresses that the type of A over B∪C does not fork over C; it generalizes linear-algebra-style independence and measures a lack of new dividing information introduced by B beyond C.

Forking independence (often abbreviated to forking) is a ternary relation a ⟂_A b (or between types) expressing that the type of a over A∪{b} does not fork over A; intuitively, a is independent from b over A when no formula in the type of a over A∪{b} divides over A. Forking formalizes a robust notion of independence relative to a complete first-order theory.