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Topological dynamics and definable groups

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Anand Pillay*
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail:a.pillay@leeds.ac.uk
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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” SG.ext(M), can explain, account for, or give rise to, the quotient G/G00, at least for suitable groups in NIP theories. We give a positive answer for measure-stable (or f sg) 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/G00 can be recovered, via the Ellis theory, from a natural Ellis semigroup structure on the space of global f-generic types.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 657 - 666
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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