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Ramsey families of subtrees of the dyadic tree

Author: Vassilis Kanellopoulos
Journal: Trans. Amer. Math. Soc. 357 (2005), 3865-3886
MSC (2000): Primary 05C05
Published electronically: May 20, 2005
MathSciNet review: 2159691
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Abstract: We show that for every rooted, finitely branching, pruned tree $T$of height $\omega$ there exists a family $\mathcal{F}$ which consists of order isomorphic to $T$ subtrees of the dyadic tree $C=\{0,1\}^{<\mathbb{N} }$ with the following properties: (i) the family $\mathcal{F}$ is a $G_\delta$ subset of $2^C$; (ii) every perfect subtree of $C$ contains a member of $\mathcal{F}$; (iii) if $K$ is an analytic subset of $\mathcal{F}$, then for every perfect subtree $S$ of $C$ there exists a perfect subtree $S'$ of $S$ such that the set $\{A\in\mathcal{F}: A\subseteq S'\}$ either is contained in or is disjoint from $K$.

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Additional Information

Vassilis Kanellopoulos
Affiliation: Department of Mathematics, National Technical University of Athens, Athens 15780, Greece

Received by editor(s): August 5, 2002
Published electronically: May 20, 2005
Additional Notes: This research was partially supported by the Thales program of NTUA
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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