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Externally definable sets and dependent pairs

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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00526000
Contributor : Artem Chernikov <>
Submitted on : Wednesday, October 13, 2010 - 1:57:45 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:13 PM

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  • HAL Id : hal-00526000, version 1
  • ARXIV : 1007.4468

Citation

Artem Chernikov, Pierre Simon. Externally definable sets and dependent pairs. 2010. ⟨hal-00526000⟩

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