Hajnal, András; Juhász, István; Soukup, L. On saturated almost disjoint families. (English) Zbl 0648.03034 Commentat. Math. Univ. Carol. 28, 629-633 (1987). 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 Cited in 1 ReviewCited in 1 Document MSC: 03E35 Consistency and independence results 03E05 Other combinatorial set theory Keywords:almost-disjoint sets; consistency; iterated addition of dominating reals PDFBibTeX XMLCite \textit{A. Hajnal} et al., Commentat. Math. Univ. Carol. 28, 629--633 (1987; Zbl 0648.03034) Full Text: EuDML