Ladder systems on trees
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- by Zoran Spasojević
- Proc. Amer. Math. Soc. 130 (2002), 193-203
- DOI: https://doi.org/10.1090/S0002-9939-01-05072-9
- Published electronically: July 31, 2001
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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.References
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Bibliographic Information
- Zoran Spasojević
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 193-203
- MSC (2000): Primary 03E05
- DOI: https://doi.org/10.1090/S0002-9939-01-05072-9
- MathSciNet review: 1626486