Submission date: 21 February 2023

Abstract:

We study the definable topological dynamics (G,S_G(M)) of a definable group acting on its type space, where M is a structure and G is a group definable in M. In [Newelski-I], Newelski raised a question of whether weakly generic types coincide with almost periodic types in definable topological dynamics. In [YZ-Sta], we introduced the notion of stationarity, showing the answer is positive when G is a stationary definably amenable group definable over the field of p-adic numbers or an o-minimal expansion of real closed field.
In this paper, we continue with the work of [YZ-Sta], focusing on the case where G is a commutative group definable over the field of p-adic numbers, and showing that weakly generic types coincide with almost periodic types if and only if either G has definable f-generics or G is stationary.

Mathematics Subject Classification: 03C98 37B05 11E95 03C64 43A07

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Full text arXiv 2302.10508: pdf, ps.