Ramsey families of subtrees of the dyadic tree

Author:
Vassilis Kanellopoulos

Journal:
Trans. Amer. Math. Soc. **357** (2005), 3865-3886

MSC (2000):
Primary 05C05

DOI:
https://doi.org/10.1090/S0002-9947-05-03968-1

Published electronically:
May 20, 2005

MathSciNet review:
2159691

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Abstract: We show that for every rooted, finitely branching, pruned tree of height there exists a family which consists of order isomorphic to subtrees of the dyadic tree with the following properties: (i) the family is a subset of ; (ii) every perfect subtree of contains a member of ; (iii) if is an analytic subset of , then for every perfect subtree of there exists a perfect subtree of such that the set either is contained in or is disjoint from .

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Additional Information

**Vassilis Kanellopoulos**

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

Email:
bkanel@math.ntua.gr

DOI:
https://doi.org/10.1090/S0002-9947-05-03968-1

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.