No CrossRef data available.
Article contents
Families of partial representing sets
Published online by Cambridge University Press: 09 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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
- Copyright
- Copyright © Australian Mathematical Society 1985
References
[1]Balanda, K. P., ‘Maximally almost disjoint families of representing sets’, Math. Proc. Cambridge Philos. Soc. 93 (1983), 1–7.Google Scholar
[2]Balanda, K. P., ‘Almost disjoint families of representing sets’, Z. Math. Logik Grundlag. Math., to appear.Google Scholar
[3]Baumgartner, J. E., ‘Almost-disjoint sets, the dense set problem and partition calculus’, Ann. Math. Logic 9 (1976), 401–439.Google Scholar
[4]Erdös, P. and Rado, R., ‘Intersection theorems for systems of sets I’, J. London Math. Soc. 44 (1969), 467–479.Google Scholar
You have
Access