External definability and groups in NIP theories

DOI10.1112/jlms/jdu019zbMath1353.03020arXiv1307.4794OpenAlexW2106715694MaRDI QIDQ2874657

Pierre Simon, Artem Chernikov, Anand Pillay

Publication date: 8 August 2014

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4794

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Classification theory, stability, and related concepts in model theory (03C45) Model theory of ordered structures; o-minimality (03C64)

Related Items (14)

Definable convolution and idempotent Keisler measures ⋮ Definably topological dynamics of \(p\)-adic algebraic groups ⋮ Invariant measures in simple and in small theories ⋮ On minimal flows and definable amenability in some distal NIP theories ⋮ Generalised Bohr compactification and model-theoretic connected components ⋮ On minimal flows, definably amenable groups, and o-minimality ⋮ Topological dynamics for groups definable in real closed field ⋮ Elementary classes of finite VC-dimension ⋮ Definably amenable NIP groups ⋮ THE ELLIS GROUP CONJECTURE AND VARIANTS OF DEFINABLE AMENABILITY ⋮ On some dynamical aspects of NIP theories ⋮ Invariant types in NIP theories ⋮ Some model theory and topological dynamics of $p$-adic algebraic groups ⋮ Topological dynamics and NIP fields

Cites Work

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• Connected components of definable groups and o-minimality. I
• On NIP and invariant measures
• Model theoretic connected components of groups
• Externally definable sets and dependent pairs
• Dependent first order theories, continued
• Generically stable and smooth measures in NIP theories
• Topological dynamics of definable group actions
• Some model theory of SL(2,R)
• Externally definable sets and dependent pairs II
• Topological dynamics and definable groups
• Forking and Dividing in NTP₂ theories
• Minimal bounded index subgroup for dependent theories
• Groups, measures, and the NIP

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