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An order property for families of sets

Part of: Set theory

Published online by Cambridge University Press:  09 April 2009

N. H. Williams
N. H. Williams
Affiliation:
Department of MathematicsUniversity of QueenslandSt. Lucia, Queensland 4067, Australia
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Abstract

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We develop the idea of a θ-ordering (where θ is an infinite cardinal) for a family of infinite sets. A θ-ordering of the family A is a well ordering of A which decomposes A into a union of pairwise disjoint intervals in a special way, which facilitates certain transfinite constructions. We show that several standard combinatorial properties, for instance that of the family A having a θ-transversal, are simple consequences of A possessing a θ-ordering. Most of the paper is devoted to showing that under suitable restrictions, an almost disjoint family will have a θ-ordering. The restrictions involve either intersection conditions on A (the intersection of every λ-size subfamily of A has size at most κ) or a chain condition on A.

MSC classification

Secondary: 03E05: Other combinatorial set theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 3 , June 1988 , pp. 294 - 310
Copyright
Copyright © Australian Mathematical Society 1988

References

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