An order property for families of sets

Williams N.H. (1988) An order property for families of sets. Journal of the Australian Mathematical Society, 44 3: 294-310. doi:10.1017/S1446788700032110


Author Williams N.H.
Title An order property for families of sets
Journal name Journal of the Australian Mathematical Society   Check publisher's open access policy
ISSN 1446-8107
Publication date 1988-01-01
Sub-type Article (original research)
DOI 10.1017/S1446788700032110
Volume 44
Issue 3
Start page 294
End page 310
Total pages 17
Subject 2600 Mathematics
Abstract 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 k) or a chain condition on A.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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Created: Tue, 23 Aug 2016, 15:33:08 EST by System User