Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :S. Anscombe, A. Khélif, A. Vignati
Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr
Salle : 1013
Adresse :Sophie Germain

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Orateur(s) Ludovic Patey - CNRS, Université Lyon 1,
Titre The computability-theoretic aspects of Milliken's tree theorem and applications
Horaire16:00 à 17:15

Milliken's tree theorem states that for every countable, finitely
branching tree T with no leaves, and every finite coloring f of the
strong subtrees of height n, there is an infinite strong subtree over
which the strong subtrees of height n are monochromatic. This theorem
has several applications, among which Devlin's theorem about finite
coloring of the rationals, and a theorem about the Rado graph. In this
talk, we give a survey of the computability-theoretic aspects of these
statements seen as mathematical problems, in terms of instances and
solutions. Our main motivation is reverse mathematics. This is a joint
work with Paul-Elliot Anglès d'Auriac, Peter Cholak and Damir Dzhafarov.

AdresseSophie Germain