Submission date: 27 July 2010.

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.

Mathematics Subject Classification: 03Cxx

Keywords and phrases: NIP, dependent theories, pairs, indiscernible sequences, externally definable sets.

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