## 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.

### MSC:

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

### Keywords:

rosy theory; NIP; stably embedded predicate

Zbl 1187.03034
Full Text:

### References:

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