Milliken's tree theorem
In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure than sets. Let T be a finitely splitting rooted tree of height ω, n a positive integer, and the collection of all strongly embedded subtrees of T of height n. In one of its simple forms, Milliken's tree theorem states that if then for some strongly embedded infinite subtree R of T, for some i ≤ r. This immediately implies Ramsey's theorem; take the tree T to be a linear ordering on ω vertices.
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Milliken's tree theorem
In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure than sets. Let T be a finitely splitting rooted tree of height ω, n a positive integer, and the collection of all strongly embedded subtrees of T of height n. In one of its simple forms, Milliken's tree theorem states that if then for some strongly embedded infinite subtree R of T, for some i ≤ r. This immediately implies Ramsey's theorem; take the tree T to be a linear ordering on ω vertices.
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In mathematics, Milliken's tre ...... rem is strongly embedded in T.
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In mathematics, Milliken's tre ...... linear ordering on ω vertices.
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Milliken's tree theorem
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