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