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Ladder Systems on Trees
Proceedings of the American Mathematical Society
Vol. 130, No. 1 (Jan., 2002), pp. 193-203
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2699729
Page Count: 11
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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.
Proceedings of the American Mathematical Society © 2002 American Mathematical Society