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Families of partial representing sets

Published online by Cambridge University Press:  09 April 2009

Kevin P. Balanda
Kevin P. Balanda
Affiliation:
Department of Mathematics University of QueenslandSt. Lucia, Qld 4067, Australia
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Abstract

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Assume GCH. Let κ, μ, Σ be cardinals, with κ infinite. Let be a family consisting of λ pairwise almost disjoint subsets of Σ each of size κ, whose union is Σ. In this note it is shown that for each μ with 1 ≤ μ ≤min(λ, Σ), there is a “large” almost disjoint family of μ-sized subsets of Σ, each member of having non-empty intersection with at least μ members of the family .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 198 - 206
Copyright
Copyright © Australian Mathematical Society 1985

References

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