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An intersection theorem of Erdős and Rado

Published online by Cambridge University Press:  24 October 2008

Roy O. Davies
Roy O. Davies
Affiliation:
The University, Leicester
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Extract

Theorem. if a ≥ 2, b ≥ 1, and a + b ≥ ℵ0, then every collection of more than ab sets each of cardinal not exceeding b contains a subcollection of more than ab sets every two of which have the same intersection.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 995 - 996
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Engelking, R. and Karłowicz, M.Some theorems of set theory and their topological consequences. Fund. Math. 57 (1965), 275–285.CrossRefGoogle Scholar
(2)Erdős, P. and Rado, R.Intersection theorems for systems of sets. J. London Math. Soc. 35 (1960), 85–90.CrossRefGoogle Scholar
(3)Marek, W.On families of sets. Bull. Acad. Pol. Sci., Sér. Sci. Math. Astr. Phys. 12 (1964), 443–448.Google Scholar
(4)Michael, E.A note on intersections. Proc. Amer. Math. Soc. 13 (1962), 281–283.CrossRefGoogle Scholar