Journal
ANNALS OF PURE AND APPLIED LOGIC
Volume 165, Issue 2, Pages 552-562Publisher
ELSEVIER
DOI: 10.1016/j.apal.2013.07.020
Keywords
NIP; Definable groups; Definable types; Compactification; Amenability; Topological dynamics
Categories
Funding
- Marie Curie Intra-European Fellowship MODGROUP [PIEF-GA-2009-254123]
- Polish Government MNiSW grant [N N201 545938]
- EPSRC [EP/I002294/1]
- Engineering and Physical Sciences Research Council [EP/I002294/1] Funding Source: researchfish
- EPSRC [EP/I002294/1] Funding Source: UKRI
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For G a group definable in some structure M, we define notions of definable compactification of G and definable action of G on a compact space X (definable G-flow), where the latter is under a definability of types assumption on M. We describe the universal definable compactification of G as G*/(G*)(00)(M) and the universal definable G-ambit as the type space S-G(M). We also point out the existence and uniqueness of universal minimal definable G-flows, and discuss issues of amenability and extreme amenability in this definable category, with a characterization of the latter. For the sake of completeness we also describe the universal (Bohr) compactification and universal G-ambit in model-theoretic terms, when G is a toPological group (although it is essentially well-known). (C) 2013 Elsevier B.V. All rights reserved.
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