English
Borel sets of Rado graphs are Ramsey
Multi angle
Auteurs : Dobrinen, Natasha (Auteur de la Conférence)
CIRM (Editeur )
03C15 - Denumerable structures
03E75 - Applications
05D10 - Ramsey theory
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2052/Slides/Dobrinen_Luminy_Sept2019.pdf
CIRM (Editeur )
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Résumé :
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.
Keywords : Rado graph; Ramsey theory; forcing
Codes MSC : Keywords : Rado graph; Ramsey theory; forcing
03C15 - Denumerable structures
03E75 - Applications
05D10 - Ramsey theory
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2052/Slides/Dobrinen_Luminy_Sept2019.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 14/10/2019 Date de captation : 25/09/2019 Sous collection : Research talks arXiv category : Combinatorics ; Logic Domaine : Logic and Foundations ; Combinatorics Format : MP4 (.mp4) - HD Durée : 00:51:19 Audience : Researchers Download : https://videos.cirm-math.fr/2019-09-25_Dobrinen.mp4 
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Informations sur la Rencontre
Nom de la rencontre : 15th International Luminy Workshop in Set Theory / XVe Atelier international de théorie des ensemblesOrganisateurs de la rencontre : Dzamonja, Mirna ; Velickovic, Boban Dates : 23/09/2019 - 27/09/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2052.html
Données de citation
DOI : 10.24350/CIRM.V.19563603Citer cette vidéo: Dobrinen, Natasha (2019). Borel sets of Rado graphs are Ramsey. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19563603 URI : http://dx.doi.org/10.24350/CIRM.V.19563603 |
Voir aussi
- [ Post-edited] Chain conditions, unbounded colorings and the $C$-sequence spectrum / Auteur de la Conférence Rinot, Assaf.
- [Multi angle] Towards the right generalization of descriptive set theory to uncountable cardinals / Auteur de la Conférence Motto Ros, Luca.
- [Multi angle] Lower bounds for the perfect set property at weakly compact cardinals / Auteur de la Conférence Müller, Sandra.
- [Multi angle] Some results on set mappings / Auteur de la Conférence Komjáth, Péter.
Bibliographie
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- DOBRINEN, Natasha. The Ramsey Theory of Henson graphs. arXiv preprint arXiv:1901.06660, 2019. - https://arxiv.org/abs/1901.06660
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