Dependence and Isolated Extensions
Logic
2011-08-31 v1
Abstract
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.
Cite
@article{arxiv.0911.1361,
title = {Dependence and Isolated Extensions},
author = {Vincent Guingona},
journal= {arXiv preprint arXiv:0911.1361},
year = {2011}
}
Comments
10 pages, 0 figures