# Almost disjoint sets

It is intuitive and easy to see that if $A$ is a countable set and $\{ A_\gamma \}_{\gamma \in \Gamma}$, where $A_\gamma \subset A$, is a disjoint collection of subsets, then $\Gamma$ is countable. (Although one has to be careful with saying “intuitive” and “easy to see” in set theory.) A natural question is, what happens if we allow the sets $A_{\gamma}$ to have nonempty but finite intersections? This question was posed in Halmos’ classic problem book Problems for Mathematicians: Young and Old, and this short post is dedicated to a few solutions.

https://nonemptyspaces.wordpress.com/2016/02/16/almost-disjoint-sets/