Chain conditions and the existence of delta-families

Williams, N. H.

doi:10.1017/s0305004100054414

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Intersection Conditions1

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1981

1988

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Cited by 2 publications

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“…H. Williams [7] THEOREM 2. This method of proof fails for larger A, though the result may still be true.…”

Section: Intersection Conditionsmentioning

confidence: 99%

An order property for families of sets

Williams

1988

J Aust Math Soc A

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We develop the idea of a ^-ordering (where 6 is an infinite cardinal) for a family of infinite sets. A 0-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 ^-transversal, are simple consequences of A possessing a 0-ordering. Most of the paper is devoted to showing that under suitable restrictions, an almost disjoint family will have a 0-ordering. The restrictions involve either intersection conditions on A (the intersection of every A-size subfamily of A has size at most K) or a chain condition on A.

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“…H. Williams [7] THEOREM 2. This method of proof fails for larger A, though the result may still be true.…”

Section: Intersection Conditionsmentioning

confidence: 99%