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Preprint Number 498

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498. Itay Kaplan and Alexander Usvyatsov
Strict independence in dependent theories
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Submission date: 20 August 2012.

Abstract:

We investigate the notions of strict independence and strict non-forking in dependent theories, establish basic properties and connections between the two. In particular it follows from our study that strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing in dependent theories. We prove simple characterizations of such sequences, as well as of Morley sequences which are witnesses. As a by-product of this investigation, we obtain information on types co-dominated by generically stable types. For example, we prove that every Morley sequence in such a type is a witness.

Mathematics Subject Classification: 03C95, 03C45

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Full text arXiv 1208.4062: pdf, ps.


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