Dependence and Isolated Extensions
arXiv:0911.1361
Abstract
In this paper, we show that ϕis a dependent formula if and only if all ϕ-types have an extension to a ϕ-isolated ϕ-type that is an "elementary ϕ-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 ϕnew elements to the domain of the original ϕ-type. We give corollaries to this theorem and discuss parallels to the stable setting.
10 pages, 0 figures