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June 2013 Topological dynamics and definable groups
Anand Pillay
J. Symbolic Logic 78(2): 657-666 (June 2013). DOI: 10.2178/jsl.7802170

Abstract

We give a commentary on Newelski's suggestion or conjecture [8] that topological dynamics, in the sense of Ellis [3], applied to the action of a definable group $G(M)$ on its “external type space” $S_{G,\textit{ext}}(M)$, can explain, account for, or give rise to, the quotient $G/G^{00}$, at least for suitable groups in NIP theories. We give a positive answer for measure-stable (or $fsg$) groups in NIP theories. As part of our analysis we show the existence of “externally definable” generics of $G(M)$ for measure-stable groups. We also point out that for $G$ definably amenable (in a NIP theory) $G/G^{00}$ can be recovered, via the Ellis theory, from a natural Ellis semigroup structure on the space of global $f$-generic types.

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Anand Pillay. "Topological dynamics and definable groups." J. Symbolic Logic 78 (2) 657 - 666, June 2013. https://doi.org/10.2178/jsl.7802170

Information

Published: June 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1278.03071
MathSciNet: MR3145201
Digital Object Identifier: 10.2178/jsl.7802170

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 2 • June 2013
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