## Separability properties of almost-disjoint families of sets.(English)Zbl 0246.05002

Several results are proved on almost disjoint sets and many new problems are raised. Among others the authors prove the following conjecture of Hechler: Let $$F$$ be a family of infinite sets $$\{A_\alpha \}$$ satisfying $$|A_{\alpha_1} \cap A_{\alpha_2}| < \aleph_0$$. Assume further that the family has chromatic number $$>2$$ (or does not have property $$B$$) i.e. if a set has a non-empty intersection with every $$A$$, then it contains at least one of them. Then there must be two $$A$$’s which are disjoint. Further in general it is not true that there are three $$A$$’s which are pairwise disjoint.

### MSC:

 05A05 Permutations, words, matrices 03E05 Other combinatorial set theory
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### References:

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