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SUMMARY:Damir Dzhafarov (U of Connecticut)
DTSTART:20200820T180000Z
DTEND:20200820T190000Z
DTSTAMP:20260423T035749Z
UID:OLS/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/19/">Mil
 liken's tree theorem and computability theory</a>\nby Damir Dzhafarov (U o
 f Connecticut) as part of Online logic seminar\n\n\nAbstract\nMilliken's t
 ree theorem is a powerful combinatorial result that generalized Ramsey's t
 heorem and many other familiar partition results. I will present recent wo
 rk on the effective and proof-theoretic strength of this theorem\, which w
 as originally motivated by a question of Dobrinen. The main result is a co
 mplete characterization of Milliken's tree theorem in terms of reverse mat
 hematics and the usual computability-theoretic hierarchies\, along with se
 veral applications to other combinatorial problems. Key to this is a new i
 nductive proof of Milliken's tree theorem\, employing an effective version
  of the Halpern-Lauchli theorem. This is joint work with Angles d'Auriac\,
  Cholak\, Monin\, and Patey.\n
LOCATION:https://researchseminars.org/talk/OLS/19/
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