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Maximally almost disjoint families of representing sets

Published online by Cambridge University Press:  24 October 2008

Kevin P. Balanda
Kevin P. Balanda
Affiliation:
University of Queensland, Australia
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Extract

A family of κ-sized sets is said to be almost disjoint if each pair of sets from the family intersect in a set of power less than κ. Such an almost disjoint family ℋ is defined to be κ-maximally almost disjoint (κ-MAD) if |∪ℋ| = κ and each κ-sized subset of ∪ ℋ intersects some member of ℋ in a set of cardinality κ. A set T is called a representing set of a family if T ⊆ ∪ and T has non-empty intersection with each member of .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 1 - 7
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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