##  [Forking Independence](/forking-independence) 

  ##  [Forking Independence](https://mathlogic.quantumdictionary.io/forking-independence-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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](https://algebra.quantumdictionary.io/forking-independence-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.