## Lajos Soukup

*{On ${\omega }^{{}^2}$-saturated families} *

Comment.Math.Univ.Carolinae 32,2 (1991) 355-359. **Abstract:**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 $\geq {\omega ^{\text {\tiny 2}}}$ contains an element of $\Cal A_{\lambda }$.

**Keywords:** almost disjoint, saturated family, refinement, large cardinals

**AMS Subject Classification:** 03E35

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