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