Ramsey Families of Subtrees of the Dyadic Tree
نویسنده
چکیده
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 2C ; (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.
منابع مشابه
A Classification of Separable Rosenthal Compacta and Its Applications
Contents 1. Introduction 2 2. Ramsey properties of perfect sets and of subtrees of the Cantor tree 8 2.1. Notations 8 2.2. Partitions of trees 9 2.3. Partitions of perfect sets 11 3. Increasing and decreasing antichains of a regular dyadic tree 11 4. Canonicalizing sequential compactness of trees of functions 14 4.1. Sequential compactness of trees of functions 14 4.2. Equivalence of families o...
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