Ramsey families of subtrees of the dyadic tree

Kanellopoulos, V

dc.contributor.author	Kanellopoulos, V	en
dc.date.accessioned	2014-03-01T01:23:00Z
dc.date.available	2014-03-01T01:23:00Z
dc.date.issued	2005	en
dc.identifier.issn	0002-9947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16763
dc.subject.classification	Mathematics	en
dc.subject.other	PARTITION THEOREM	en
dc.subject.other	INFINITE SUBTREES	en
dc.subject.other	SETS	en
dc.subject.other	COMBINATORICS	en
dc.subject.other	PROOF	en
dc.title	Ramsey families of subtrees of the dyadic tree	en
heal.type	journalArticle	en
heal.identifier.primary	10.1090/S0002-9947-05-03968-1	en
heal.identifier.secondary	http://dx.doi.org/10.1090/S0002-9947-05-03968-1	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We show that for every rooted, finitely branching, pruned tree T of height ω there exists a family ℱ which consists of order isomorphic to T subtrees of the dyadic tree C = {0,1}<N with the following properties: (i) the family ℱ is a Gδ subset of 2 C; (ii) every perfect subtree of C contains a member of ℱ; (iii) if K is an analytic subset of ℱ, then for every perfect subtree S of C there exists a perfect subtree S' of S such that the set {A ∈ ℱ : A ⊆ S'} either is contained in or is disjoint from K. © 2005 American Mathematical Society.	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	Transactions of the American Mathematical Society	en
dc.identifier.doi	10.1090/S0002-9947-05-03968-1	en
dc.identifier.isi	ISI:000230719300002	en
dc.identifier.volume	357	en
dc.identifier.issue	10	en
dc.identifier.spage	3865	en
dc.identifier.epage	3886	en