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Borel sets of Rado graphs are Ramsey
Multi angle
Authors : Dobrinen, Natasha (Author of the conference)
CIRM (Publisher )
03C15 - Denumerable structures
03E75 - Applications
05D10 - Ramsey theory
Additional resources :
https://www.cirm-math.fr/RepOrga/2052/Slides/Dobrinen_Luminy_Sept2019.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : Keywords : Rado graph; Ramsey theory; forcing
03C15 - Denumerable structures
03E75 - Applications
05D10 - Ramsey theory
Additional resources :
https://www.cirm-math.fr/RepOrga/2052/Slides/Dobrinen_Luminy_Sept2019.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/10/2019 Conference Date : 25/09/2019 Subseries : Research talks arXiv category : Combinatorics ; Logic Mathematical Area(s) : Logic and Foundations ; Combinatorics Format : MP4 (.mp4) - HD Video Time : 00:51:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-09-25_Dobrinen.mp4 
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Information on the Event
Event Title : 15th International Luminy Workshop in Set Theory / XVe Atelier international de théorie des ensemblesEvent Organizers : Dzamonja, Mirna ; Velickovic, Boban Dates : 23/09/2019 - 27/09/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2052.html
Citation Data
DOI : 10.24350/CIRM.V.19563603Cite this video as: 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 |
See Also
- [Post-edited] Chain conditions, unbounded colorings and the $C$-sequence spectrum / Author of the conference Rinot, Assaf.
- [Multi angle] Towards the right generalization of descriptive set theory to uncountable cardinals / Author of the conference Motto Ros, Luca.
- [Multi angle] Lower bounds for the perfect set property at weakly compact cardinals / Author of the conference Müller, Sandra.
- [Multi angle] Some results on set mappings / Author of the conference Komjáth, Péter.
Bibliography
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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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