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On saturated almost disjoint families. (English) Zbl 0648.03034
The consistency of the following statement is proven. For every uncountable set X there is an almost-disjoint family F of countably infinite subsets of X such that every subset Y of X which cannot be covered by finitely many members of F plus a finite set contains a subset which is in F. The very clever argument uses iterated addition of dominating reals of length \(\omega_ 1\).
Reviewer: P.Komjáth

MSC:
03E35 Consistency and independence results
03E05 Other combinatorial set theory
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