Nip超图的可定义正则引理

IF 0.6 4区数学 Q3 MATHEMATICS

Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI:10.1093/qmath/haab011

Artem Chernikov;Sergei Starchenko

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引用次数: 25

摘要

我们系统地研究了NIP超图的正则现象以及与(局部)一般稳定测度理论的联系，提供了关于有界vc维图的Alon-Fischer-Newman和Lovász-Szegedy结果的模型理论超图版本。我们还考虑了稳定超图和远端超图正则性的两种极端情况，改进和推广了文献中关于图的相应结果。最后，我们考虑了NIP超图的大(近似)齐次可定义子集的存在性问题，并给出了一些正结果和反例，特别是对于在p-adics中可定义的图。

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Definable Regularity Lemmas for Nip Hypergraphs

We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hypergraph version of the results of Alon-Fischer-Newman and Lovász-Szegedy for graphs of bounded VC-dimension. We also consider the two extremal cases of regularity for stable and distal hypergraphs, improving and generalizing the corresponding results for graphs in the literature. Finally, we consider a related question of the existence of large (approximately) homogeneous definable subsets of NIP hypergraphs and provide some positive results and counterexamples, in particular for graphs definable in the p-adics.

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来源期刊

Quarterly Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.