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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Topological Ramsey theory of countable ordinals

## Topological Ramsey theory of countable ordinalsAdd to your list(s) Download to your calendar using vCal - Hilton, J (University of Leeds)
- Saturday 10 October 2015, 13:00-13:55
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact webseminars. Mathematical, Foundational and Computational Aspects of the Higher Infinite Recall that the Ramsey number R(n, m) is the least k such that, whenever the edges of the complete graph on k vertices are coloured red and blue, then there is either a complete red subgraph on n vertices or a complete blue subgraph on m vertices – for example, R(4, 3) = 9. This generalises to ordinals: given ordinals $lpha$ and $eta$, let $R(lpha, eta)$ be the least ordinal $gamma$ such that, whenever the edges of the complete graph with vertex set $gamma$ are coloured red and blue, then there is either a complete red subgraph with vertex set of order type $lpha$ or a complete blue subgraph with vertex set of order type $eta$ —- for example, $R(omega 1, 3) = omega 1$. We will prove the result of Erdos and Milner that $R(lpha, k)$ is countable whenever $lpha$ is countable and k is finite, and look at a topological version of this result. This is joint work with Andres Caicedo. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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