Publications > Preprint server > Preprint Number 2568
Preprint Number 2568
2568. Artem Chernikov and Henry Towsner Perfect stable regularity lemma and slice-wise stable hypergraphs E-mail: Submission date: 12 February 2024 Abstract: We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of vertices. On the one hand, we provide a complete classification of the various possibilities in the ternary case. On the other hand, we provide an example of a family of slice-wise stable 3-hypergraphs so that for no partition of the vertices, any triple of parts has density close to 0 or 1. In particular, this addresses some questions and conjectures of Terry and Wolf. We work in the general measure theoretic context of graded probability spaces, so all our results apply both to measures in ultraproducts of finite graphs, leading to the aforementioned combinatorial applications, and to commuting definable Keisler measures, leading to applications in model theory. Mathematics Subject Classification: 03C45, 05C35, 05C65, 05C75 Keywords and phrases: |
Last updated: March 5 2024 19:01 | Please send your corrections to: |