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Chain conditions and the existence of delta-families

Published online by Cambridge University Press:  24 October 2008

N. H. Williams
N. H. Williams
Affiliation:
University of Queensland, Brisbane
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Extract

Let = (Ai;i ∈ I) be an indexed family of sets. The family is said to contain the family = (Bj;j ∈ J) if there is a one-to-one map f from J into I such that Bj = Af(i) for all j in J. The indexed family = (Ai;i ∈ I) is said to be a Δ (λ)-family if |I| = λ and Ai ∩ Aj = Ak ∩ Ai for all pairs i, j and k, l from I. The family is said to be a (λ, k)-family if |I| = λ and |Ai| = k for all Ai.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 167 - 179
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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