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Stable embeddedness and NIP

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Anand Pillay*
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail: [email protected]
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Abstract

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]).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 665 - 672
Copyright
Copyright © Association for Symbolic Logic 2011

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References

REFERENCES

[1]Adler, H., A geometric introduction to forking and thorn forking, 2007, preprint.Google Scholar
[2]Adler, H., Introduction to theories without the independence property, Archive for Mathematical Logic, to appear.Google Scholar
[3]Chernikov, A. and Kaplan, I., Forking and dividing in NTP2 theories, to appear in this Journal, number 147 on the MODNET preprint server.Google Scholar
[4]Ealy, C., Krupinski, K., and Pillay, A., Superrosy dependent groups having finitely satisfiable generics, Annals of Pure and Applied Logic, vol. 151 (2008), pp. 1–21.CrossRefGoogle Scholar
[5]Ealy, C. and Onshuus, A., Characterizing rosy theories, this Journal, vol. 72 (2007), pp. 919–940.Google Scholar
[6]Hasson, A. and Onshuus, A., Embedded o-minimal structures, Bulletin of the London Mathematical Society, vol. 42 (2010), pp. 64–74.CrossRefGoogle Scholar
[7]Hrushovski, E. and Pillay, A., On NIP and invariant measures, preprint 2009 (revised version), http://arxiv.org/abs/0710.2330.Google Scholar
[8]Onshuus, A., Properties and consequences of thorn independence, this Journal, vol. 71 (2006), pp. 1–21.Google Scholar
[9]Poizat, B., A course in model theory; an introduction to contemporary mathematical logic, Springer, 2000.Google Scholar
[10]Shelah, S., Dependent first order theories, continued, Israel Journal of Mathematics, vol. 173 (2009), pp. 1–60.CrossRefGoogle Scholar
[11]Usvyatsov, A., Morley sequences in dependent theories, preprint, http://arxiv.org/abs/0810.0733.Google Scholar