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Stable embeddedness and NIP

Published online by Cambridge University Press:  12 March 2014

Anand Pillay*
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail:


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 [6] 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 ([3], [10]).

Research Article
Copyright © Association for Symbolic Logic 2011

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