On Descent and germs
Pierre Simon, Mariana Vicaria

TL;DR
This paper introduces a simplified proof of descent for stably dominated types in various theories, removes previous assumptions, and explores properties of stable sets in NIP theories, with applications to ACVF.
Contribution
It provides a new, simpler proof of descent for stably dominated types and extends the understanding of stable sets in NIP theories, correcting prior results.
Findings
Simplified proof of descent for stably dominated types
Descent proof in ACVF without global invariant extensions
Stable sets in NIP theories have bounded stabilizing property
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 . Furthermore, we demonstrate that any stable set in an 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 .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Logic, programming, and type systems · Advanced Graph Theory Research
