Externally definable sets and dependent pairs

Details Externally definable sets and dependent pairs Externally definable sets and dependent pairs

2010-07-26

arxiv.org/abs/1007.4468v2

Mathematics

Logic

17 pages, some typos and mistakes corrected, overall presentation improved, more details for the examples are given

Scientific paper

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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