Pillay, Anand Stable embeddedness and NIP. (English) Zbl 1220.03020 J. Symb. Log. 76, No. 2, 665-672 (2011). 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. Cited in 6 Documents MSC: 03C45 Classification theory, stability, and related concepts in model theory Keywords:rosy theory; NIP; stably embedded predicate Citations:Zbl 1187.03034 PDFBibTeX XMLCite \textit{A. Pillay}, J. Symb. Log. 76, No. 2, 665--672 (2011; Zbl 1220.03020) Full Text: DOI arXiv References: [1] A course in model theory; an introduction to contemporary mathematical logic (2000) [2] Properties and consequences of thorn independence 71 pp 1– (2006) · Zbl 1103.03036 [3] DOI: 10.1112/blms/bdp098 · Zbl 1187.03034 · doi:10.1112/blms/bdp098 [4] DOI: 10.1007/s11856-009-0082-1 · Zbl 1195.03040 · doi:10.1007/s11856-009-0082-1 [5] DOI: 10.1016/j.apal.2007.09.004 · Zbl 1144.03025 · doi:10.1016/j.apal.2007.09.004 [6] Archive for Mathematical Logic [7] Characterizing rosy theories 72 pp 919– (2007) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.