Almost disjoint family on a regular cardinal
= Almost disjoint family on a regular cardinal
{title2=$A\ne B\ \Longrightarrow\ |A\cap B|<\kappa$}
A family of size-$\kappa$ <subsets> of a set is almost disjoint at $\kappa$ when distinct members have intersection of size less than $\kappa$. Graphs of a <long chain under eventual domination> give such a family of size $\kappa^+$ on $\kappa\times\kappa$. Transport by a <bijection> gives a family on $\kappa$ itself.