About: Milliken's tree theorem

An Entity of Type: Abstraction100002137, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

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.

Property Value
dbo: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. (en)
dbo:wikiPageID
  • 4317775 (xsd:integer)
dbo:wikiPageLength
  • 2589 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1097298715 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdf:type
rdfs: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. 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. (en)
rdfs:label
  • Milliken's tree theorem (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License