Externally definable sets and dependent pairs

By Artem Chernikov, Pierre Simon. Israel Journal of Mathematics, 2010

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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.

Subfields: Computational Theory and Mathematics, Experimental and Cognitive Psychology, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cf675f4bd4d01de6ea7f0299ab64110d167c1f23