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