Externally definable sets and dependent pairs

Externally definable sets and dependent pairs

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...

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Veröffentlicht in:Israel journal of mathematics 2013-03, Vol.194 (1), p.409-425
Hauptverfasser: Chernikov, Artem, Simon, Pierre
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Zusammenfassung: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-012-0061-9