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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 285.04002

**Autor: ** Erdös, Paul; Hajnal, András

**Title: ** Some remarks on set theory. XI. (In English)

**Source: ** Fundam. Math. 81, 261-265 (1974).

**Review: ** The authors solve the following problem: Let |S| = m determine the largest cardinal f(m) so that if A_{\alpha} \subset S, |A_{\alpha}| < m, are subsets of S no one of which contains any other one can always find m of the sets A_{\alpha} whose union has a complement of size \geq f(m). The author determines f(m) for every infinite cardinal m, e.g. f(\aleph_{0}) = \aleph_{0}.

**Classif.: ** * 04A10 Ordinal and cardinal numbers; generalizations

04A20 Combinatorial set theory

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