Let {\displaystyle p(x)} be a complete type over some set of parameters {\displaystyle B}, and let {\displaystyle A} be a subset of {\displaystyle B}. One says that {\displaystyle p(x)} splits over {\displaystyle A} if {\displaystyle \phi (x;b_{1})\in p(x),\quad \phi (x;b_{2})\notin p(x)} for some formula {\displaystyle \phi (x;y)}, and {\displaystyle b_{1},b_{2}\in B} having the same type over {\displaystyle A}. Splitting is a weaker condition than dividing, so not splitting is a stronger condition than not dividing. If {\displaystyle M} is a sufficiently saturated model containing {\displaystyle A}, (for example, the monster model), then {\displaystyle p\in S(M)} doesn't split over {\displaystyle A} if and only if {\displaystyle p} is {\displaystyle \operatorname {Aut} (M/A)}-invariant. ::: ::: :::