Ramsey families of subtrees of the dyadic tree

Vassilis Kanellopoulos
2005 Transactions of the American Mathematical Society  
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 G δ 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
more » ... ned in or is disjoint from K.
doi:10.1090/s0002-9947-05-03968-1 fatcat:mknbaynigjflnowf3mc62bdy7y