On Descent and germs

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 $\text{ACVF}$. Furthermore, we demonstrate that any stable set in an $\text{NIP}$ 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 $\text{ACVF}$.