Submission date: 27 July 2024

Abstract:

We present a new proof of descent for stably dominated types in any theory, weakening the hypothesis of the existence of global invariant extensions. Additionally, we give a much simpler proof of descent for stably dominated types in ACVF. Furthermore, we demonstrate that any stable set in an NIP theory has the bounded stabilizing property. This result is subsequently used to correct Proposition 6.7 from the book on stable domination and independence in ACVF.

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Full text arXiv 2407.19336: pdf, ps.