# zbMATH — the first resource for mathematics

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:
 3e+35 Consistency and independence results 300000 Other combinatorial set theory
Full Text: