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Keywords:
almost disjoint; saturated family; refinement; large cardinals
almost disjoint; saturated family; refinement; large cardinals
Summary:
If there is no inner model with measurable cardinals, then for each cardinal $\lambda $ there is an almost disjoint family $\Cal A_{\lambda}$ of countable subsets of $\lambda $ such that every subset of $\lambda $ with order type $\geq {\omega^{\scriptscriptstyle2}}$ contains an element of $\Cal A_{\lambda}$.
References:
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[{4}] Goldstern M., Judah H., Shelah S.: Saturated families, and more on regular spaces omitting cardinals. preprint. MR 1052573
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