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Preprint Number 212
212. Vincent Guingona
Dependence and Isolated Extensions
Submission date: 6 November 2009.
In this paper, we show that φ is 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 φ new elements to the domain of the original φ-type. We give corollaries to this theorem and discuss parallels to the stable setting.
Mathematics Subject Classification: 03C45
Keywords and phrases: NIP, dependent, isolated, types
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