Annals of Pure and Applied Logic 165 (2):552-562 (2014)

Abstract
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 , where the latter is under a definability of types assumption on M. We describe the universal definable compactification of G as View the MathML source and the universal definable G-ambit as the type space SG. 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 compactification and universal G-ambit in model-theoretic terms, when G is a topological group
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DOI 10.1016/j.apal.2013.07.020
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References found in this work BETA

Topological Dynamics of Definable Group Actions.Ludomir Newelski - 2009 - Journal of Symbolic Logic 74 (1):50-72.
Topological Dynamics and Definable Groups.Anand Pillay - 2013 - Journal of Symbolic Logic 78 (2):657-666.

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Citations of this work BETA

Topological Dynamics for Groups Definable in Real Closed Field.Ningyuan Yao & Dongyang Long - 2015 - Annals of Pure and Applied Logic 166 (3):261-273.
Definable Topological Dynamics and Real Lie Groups.Grzegorz Jagiella - 2015 - Mathematical Logic Quarterly 61 (1-2):45-55.
Topological Dynamics of Stable Groups.Ludomir Newelski - 2014 - Journal of Symbolic Logic 79 (4):1199-1223.
Definable Topological Dynamics.Krzysztof Krupiński - 2017 - Journal of Symbolic Logic 82 (3):1080-1105.

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