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Ladder systems on trees


Author: Zoran Spasojevic
Journal: Proc. Amer. Math. Soc. 130 (2002), 193-203
MSC (2000): Primary 03E05
DOI: https://doi.org/10.1090/S0002-9939-01-05072-9
Published electronically: July 31, 2001
MathSciNet review: 1626486
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Abstract: We formulate the notion of uniformization of colorings of ladder systems on subsets of trees. We prove that Suslin trees have this property and also Aronszajn trees in the presence of Martin's Axiom. As an application we show that if a tree has this property, then every countable discrete family of subsets of the tree can be separated by a family of pairwise disjoint open sets. Such trees are then normal and hence countably paracompact. As a dual result for special Aronszajn trees we prove that the weak diamond, $\Phi _{\omega }$, implies that no special Aronszajn tree can be countably paracompact.


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Additional Information

Zoran Spasojevic
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

DOI: https://doi.org/10.1090/S0002-9939-01-05072-9
Received by editor(s): June 5, 1996
Received by editor(s) in revised form: May 18, 1998
Published electronically: July 31, 2001
Communicated by: Andreas R. Blass
Article copyright: © Copyright 2001 American Mathematical Society

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