Externally definable sets and dependent pairs
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We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah’s expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then used to prove a general theorem on dependent pairs, which in particular answers a question of Baldwin and Benedikt on naming an indiscernible sequence.
KeywordsDependent Theory Dense Pair Unary Predicate Dependent Pair Elementary Extension
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- [Adl08]H. Adler, An introduction to theories without the independence property, Archive for Mathematical Logic, to appear.Google Scholar
- [Ber]A. Berenstein, Lovely pairs and dense pairs of o-minimal structures, submitted.Google Scholar
- [vdDL95]L. van den Dries and A. H. Lewenberg, T-convexity and tame extensions, Journal of Symbolic Logic 155 (1995), 807–836.Google Scholar
- [EP05]A. J. Engler and A. Prestel, Valued Dields, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005.Google Scholar
- [Goo09]J. Goodrick, A monotonicity theorem for dp-minimal densely ordered groups, Journal of Symbolic Logic, 2009, to appear.Google Scholar
- [Hod93]W. Hodges, Model Theory, Encyclopedia of Mathematics and its Applications, Vol. 42, Cambridge University Press, Great Britain, 1993.Google Scholar
- [Pil07]A. Pillay, On externally definable sets and a theorem of Shelah, Felgner Festchrift, Studies in Logic, College Publications, 2007.Google Scholar
- [She05]S. Shelah, Strongly dependent theories, 2005, arXiv:math.LO/0504197.Google Scholar