Milliken's Tree Theorem

Milliken's tree theorem is a partition theorem generalizing Ramsey's theorem from sets to infinite trees, structures with more organization than plain sets. It states that for a finitely splitting rooted tree of height omega, if the collection of its strongly embedded finite subtrees of a fixed size is split into finitely many color classes, some strongly embedded infinite subtree of the original tree has all of its same-sized subtrees falling into a single color class; treating a linear order as a degenerate tree shows Milliken's theorem implies Ramsey's theorem as a special case. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/