Milliken's tree theorem
id:
milliken-s-tree-theorem-258-1020631
title:
Milliken's tree theorem
text:
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 S T n 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 S T n = C 1 ∪ . . . ∪ C r then for some strongly embedded infinite subtree R of T, S R n ⊂ C i for some i ≤ r.
brand slug:
wiki
category slug:
encyclopedia
description:
Theorem in combinatorics generalizing Ramsey's theorem to infinite trees
original url:
https://en.wikipedia.org/wiki/Milliken%27s_tree_theorem
date created:
date modified:
2022-07-09T22:23:12Z
main entity:
{"identifier":"Q6859627","url":"https://www.wikidata.org/entity/Q6859627"}
image:
fields total:
13
integrity:
14