Israel Journal of Mathematics

, Volume 194, Issue 1, pp 409–425 | Cite as

Externally definable sets and dependent pairs

  • Artem ChernikovEmail author
  • Pierre Simon


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.


Dependent Theory Dense Pair Unary Predicate Dependent Pair Elementary Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Institut Camille JordanUniversité Claude Bernard — Lyon 1Villeurbanne CedexFrance
  2. 2.Département de mathématiquesEcole Normale SupérieureParis Cedex 05France

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