Externally definable sets and dependent pairs

2010/07/26 by Artem Chernikov, Pierre Simon, Chernikov, Artem +1 · 11 citations
Mathematics · Computer Science · Psychology · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Philosophy and Theoretical Science

paper · doi:10.1007/s11856-012-0061-9

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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