Résume  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 computabilitytheoretic 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 PaulElliot Anglès d'Auriac, Peter Cholak and Damir Dzhafarov.
