Milliken's tree theorem is a result in the field of combinatorial set theory, specifically in the area of Ramsey theory. It deals with properties of certain types of trees, which are hierarchical structures that can be thought of as branching diagrams. The theorem states that for any finite coloring of the nodes of a tree, one can find a subtree of a certain structure that is monochromatic (i.e., all nodes in that subtree have the same color) and satisfies certain conditions.

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