On Descent and germs

Pierre Simon; Mariana Vicaria

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arXiv · 2407.19336

On Descent and germs

Pierre Simon·Mariana Vicaria

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Abstract

We present a new proof of descent for stably dominated types in any theory, dropping 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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Pierre Simon, Mariana Vicaria. 2024-07-27. On Descent and germs. https://arxiv.org/abs/2407.19336

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