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Borel sets of Rado graphs are Ramsey

De Natasha Dobrinen

Apparaît dans la collection : 15th International Luminy Workshop in Set Theory / XVe Atelier international de théorie des ensembles

The Galvin-Prikry theorem states that Borel partitions of the Baire space are Ramsey. Thus, given any Borel subset $\chi$ of the Baire space and an infinite set $N$, there is an infinite subset $M$ of $N$ such that $\left [M \right ]^{\omega }$ is either contained in $\chi$ or disjoint from $\chi$ . In their 2005 paper, Kechris, Pestov and Todorcevic point out the dearth of similar results for homogeneous relational structures. We have attained such a result for Borel colorings of copies of the Rado graph. We build a topological space of copies of the Rado graph, forming a subspace of the Baire space. Using techniques developed for our work on the big Ramsey degrees of the Henson graphs, we prove that Borel partitions of this space of Rado graphs are Ramsey.

Informations sur la vidéo

Date de captation 25/09/2019
Date de publication 14/10/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19563603
Citer cette vidéo Dobrinen, Natasha (25/09/2019). Borel sets of Rado graphs are Ramsey. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19563603
URL https://dx.doi.org/10.24350/CIRM.V.19563603

Domaine(s)

Bibliographie

DOBRINEN, Natasha. Borel sets of Rado graphs and Ramsey's Theorem. arXiv preprint arXiv:1904.00266, 2019. - https://arxiv.org/abs/1904.00266
DOBRINEN, Natasha. The Ramsey theory of the universal homogeneous triangle-free graph. arXiv preprint arXiv:1704.00220, 2017. - https://arxiv.org/abs/1704.00220
DOBRINEN, Natasha. The Ramsey Theory of Henson graphs. arXiv preprint arXiv:1901.06660, 2019. - https://arxiv.org/abs/1901.06660
ELLENTUCK, Erik. A new proof that analytic sets are Ramsey. The Journal of Symbolic Logic, 1974, vol. 39, no 1, p. 163-165. - https://doi.org/10.2307/2272356
GALVIN, Fred et PRIKRY, Karel. Borel sets and Ramsey's theorem 1. The Journal of Symbolic Logic, 1973, vol. 38, no 2, p. 193-198. - https://doi.org/10.2307/2272055
HALPERN, James D. et LÄUCHLI, Hans. A partition theorem. Transactions of the American Mathematical society, 1966, vol. 124, no 2, p. 360-367. - https://doi.org/10.1090/s0002-9947-1966-0200172-2
LAFLAMME², Claude, SAUER, Norbert W., et VUKSANOVIC, Vojkan. Canonical partitions of universal structures. Combinatorica, 2006, vol. 26, no 2, p. 183-205. - https://doi.org/10.1007/s00493-006-0013-2
KECHRIS, Alexander S., PESTOV, Vladimir G., et TODORCEVIC, Stevo. Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups. Geometric and Functional Analysis, 2005, vol. 15, no 1, p. 106-189. - https://doi.org/10.1007/s00039-005-0503-1
MILLIKEN, Keith R. A Ramsey theorem for trees. Journal of Combinatorial Theory, Series A, 1979, vol. 26, no 3, p. 215-237. - https://doi.org/10.1016/0097-3165(79)90101-8

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/2052/Slides/Dobrinen_Luminy_Sept2019.pdf

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