English

On Descent and germs

Logic 2025-12-16 v3

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\ACVF. Furthermore, we demonstrate that any stable set in an \NIP\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\ACVF.

Keywords

Cite

@article{arxiv.2407.19336,
  title  = {On Descent and germs},
  author = {Pierre Simon and Mariana Vicaria},
  journal= {arXiv preprint arXiv:2407.19336},
  year   = {2025}
}

Comments

Second version: We were able to drop all hypothesis in the statement (also the assumption of the existence of a non-dividing sequence, required in our previous version). A third version is uploaded including details of a number of steps upon request of the referee. Current version 50 pages

R2 v1 2026-06-28T17:55:38.429Z