Stable embeddedness and NIP. (English) Zbl 1220.03020

Summary: We give some sufficient conditions for a predicate \(\mathcal P\) in a complete theory \(T\) to be “stably embedded”. Let \(\mathcal P\) be \(P\) with its “induced \(\emptyset \)-definable structure”. The conditions are that \(\mathcal P\) (or rather its theory) is “rosy”, \(P\) has NIP in \(T\) and that \(P\) is stably 1-embedded in \(T\). This generalizes a recent result of A. Hasson and A. Onshuus [Bull. Lond. Math. Soc. 42, No. 1, 64–74 (2010; Zbl 1187.03034)] which deals with the case where \(P\) is o-minimal in \(T\). Our proofs make use of the theory of strict nonforking and weight in NIP theories.


03C45 Classification theory, stability, and related concepts in model theory


Zbl 1187.03034
Full Text: DOI arXiv


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