Israel Journal of Mathematics

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

Externally definable sets and dependent pairs

Article

Abstract

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.

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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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