Consequences of Dependent Dividing on Burden
Yuki Takahashi
TL;DR
This paper explores the implications of dependent dividing in theories, showing it aligns the burden with dp-rank, proves sub-additivity of burden, and connects it to dual VC density.
Contribution
It establishes that dependent dividing causes the burden to match dp-rank and proves the burden's sub-additivity, linking it to dual VC density.
Findings
Burden equals dp-rank in theories with dependent dividing
Burden is sub-additive under dependent dividing
Connection established between burden and dual VC density
Abstract
If has dependent dividing, then the burden agrees with the dp-rank witnessed by NIP formulas. We use this observation to prove that if has dependent dividing, then the burden is sub-additive. We also state a connection between the burden and the dual VC density.
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 · Advanced Banach Space Theory · Limits and Structures in Graph Theory