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Ladder Systems on Trees

Zoran Spasojevic
Proceedings of the American Mathematical Society
Vol. 130, No. 1 (Jan., 2002), pp. 193-203
Stable URL: http://www.jstor.org/stable/2699729
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Ladder Systems on Trees
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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, Φω, implies that no special Aronszajn tree can be countably paracompact.

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