  In this paper, we show that \phi is a dependent formula if and only if all
\phi-types have an extension to a \phi-isolated \phi-type that is an
"elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we
show that the domain of this extension adds at most 2 times the independence
dimension of \phi new elements to the domain of the original \phi-type. We give
corollaries to this theorem and discuss parallels to the stable setting.
