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- Milliken's_tree_theorem abstract "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. Define where T ranges over finitely splitting rooted trees of height ω. Milliken's tree theorem says that not only is partition regular for each n < ω, but that the homogeneous subtree R guaranteed by the theorem is strongly embedded in T.".
- Milliken's_tree_theorem wikiPageID "4317775".
- Milliken's_tree_theorem wikiPageRevisionID "597581167".
- Milliken's_tree_theorem hasPhotoCollection Milliken's_tree_theorem.
- Milliken's_tree_theorem subject Category:Ramsey_theory.
- Milliken's_tree_theorem subject Category:Theorems_in_discrete_mathematics.
- Milliken's_tree_theorem subject Category:Trees_(set_theory).
- Milliken's_tree_theorem type Abstraction100002137.
- Milliken's_tree_theorem type Communication100033020.
- Milliken's_tree_theorem type Message106598915.
- Milliken's_tree_theorem type Proposition106750804.
- Milliken's_tree_theorem type Statement106722453.
- Milliken's_tree_theorem type Theorem106752293.
- Milliken's_tree_theorem type TheoremsInDiscreteMathematics.
- Milliken's_tree_theorem comment "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.".
- Milliken's_tree_theorem label "Milliken's tree theorem".
- Milliken's_tree_theorem sameAs m.0bwsbz.
- Milliken's_tree_theorem sameAs Q6859627.
- Milliken's_tree_theorem sameAs Q6859627.
- Milliken's_tree_theorem sameAs Milliken's_tree_theorem.
- Milliken's_tree_theorem wasDerivedFrom Milliken's_tree_theorem?oldid=597581167.
- Milliken's_tree_theorem isPrimaryTopicOf Milliken's_tree_theorem.