Geodesic
On $\omega^2$-saturated families
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 355-359.

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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 $\Cal A_{\lambda}$.
Classification : 03E05, 03E35, 03E55
Keywords: almost disjoint; saturated family; refinement; large cardinals 
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     title = {On $\omega^2$-saturated families},
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Soukup, Lajos. On $\omega^2$-saturated families. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 355-359. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a16/