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SUMMARY:Paul-Elliot Angles d'Auriac (University of Lyon)
DTSTART:20201006T130000Z
DTEND:20201006T140000Z
DTSTAMP:20260423T004819Z
UID:CTA/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/31/">The
  computable strength of Milliken's Tree Theorem and applications</a>\nby P
 aul-Elliot Angles d'Auriac (University of Lyon) as part of Computability t
 heory and applications\n\n\nAbstract\nDevlin's theorem and the Rado graph 
 theorem are both variants of Ramsey's theorem\, where a structure is added
  but more colors are allowed: Devlin's theorem (respectively the Rado grap
 h theorem) states if S is ℚ (respectively G\, the Rado graph)\, then for
  any size of tuple n\, there exists a number of colors l such that for any
  coloring of [S]^n into finitely many colors\, there exists a subcopy of S
  on which the coloring takes at most l colors. Moreover\, given n\, the op
 timal l is specified.\n\nThe key combinatorial theorem used in both the pr
 oof of Devlin's theorem and the Rado graph theorem is Milliken's tree theo
 rem. Milliken's tree theorem is also a variant of Ramsey's theorem\, but t
 his time for trees and strong subtrees: it states that given a coloring of
  the strong subtrees of height n of a tree T\, there exists a strong subtr
 ee of height ω of T on which the coloring is constant.\n\nIn this talk\, 
 we review the links between those theorems\, and present the recent result
 s on the computable strength of Milliken's tree theorem and its applicatio
 ns Devlin and the Rado graph theorem\, obtained with Cholak\, Dzhafarov\, 
 Monin and Patey.\n
LOCATION:https://researchseminars.org/talk/CTA/31/
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