According to Wolfram MathWorld, a collection of sets $A_1, A_2, \ldots, A_n$ is said to be disjoint if $A_i \cap A_j = \emptyset$ for all $i \ne j$. In other words, 'disjoint' refers only to 'pairwise disjoint'.
I am looking for a name for a collection of sets where $A_1 \cap A_2 \ldots \cap A_n = \emptyset$ but the sets are not necessarily pairwise disjoint. I was hoping there would be a term like 'qualifier disjoint' to refer to this.
For example, $\{0,1\}, \{0,2\}$ and $\{1,2\}$ are not pairwise disjoint, but the intersection of all three sets is empty.
If there's not an accepted name for this, how should I best express the concept in writing (given that I will need to refer to it many times)?