Forking extension

This can be used to extend the notions of linear or algebraic independence to stable theories.

These concepts were introduced by S. Shelah.

Suppose that A and B are models of some complete ω-stable theory T. If p is a type of A and q is a type of B containing p, then q is called a forking extension of p if its Morley rank is smaller, and a nonforking extension if it has the same Morley rank.

Let T be a stable complete theory.

The non-forking relation ≤ for types over T is the unique relation that satisfies the following axioms: This applied mathematics–related article is a stub.