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/
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Source Milliken's tree theorem (Wikipedia)
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1. Milliken's tree theorem (Wikipedia)
In Branch: Combinatorics, Lead sentenceQuote, In Branch: Combinatorics, Lead sentence
In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, o
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