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SUMMARY:Topological Ramsey theory of countable ordinals - Hilton\, J (Univ
 ersity of Leeds)
DTSTART:20151010T120000Z
DTEND:20151010T125500Z
UID:TALK61445@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Recall that the Ramsey number R(n\, m) is the least k such tha
 t\, whenever the edges of the complete graph on k vertices are coloured re
 d 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 t
 he 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 $l
 pha$ or a complete blue subgraph with vertex set of order type $eta$\n---
  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 cou
 ntable and k is finite\, and look at a topological version of this result.
  This is joint work with Andres Caicedo.\n
LOCATION:Seminar Room 1\, Newton Institute
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