For a set , let denote the cardinality of . A family is called strongly almost disjoint if there is an such that for any two distinct elements , of . It is shown in (without the axiom of choice) that, for all infinite sets and all strongly almost disjoint families , and there are no finite-to-one functions from into , where denotes the power set of .
"A Note on Strongly Almost Disjoint Families." Notre Dame J. Formal Logic 61 (2) 227 - 231, May 2020. https://doi.org/10.1215/00294527-2020-0002