We give some sufficient conditions for a predicate P in a complete theory T to be “stably embedded”. Let be P with its “induced ∅-definable structure”. The conditions are that (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 Hasson and Onshuus  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 (, ).
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