Dependence and Isolated Extensions

Details Dependence and Isolated Extensions Dependence and Isolated Extensions

2009-11-06

arxiv.org/abs/0911.1361v1

Proceedings of the American Mathematical Society, 139 (2011), 3349-3357

Mathematics

Logic

10 pages, 0 figures

Scientific paper

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.

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