Name for collection of sets whose intersection is empty but where sets are not necessarily pairwise disjoint 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)?
 A: For events in probability theory, Wikipedia calls events jointly or collectively exhaustive if their union is everything.
So the dual notion that their intersection is empty could be called "jointly disjoint" or "collectively disjoint".
Related question with terminology: Confusion on pairwise disjoint and disjoint
A: According to my advanced probability professor, 
sets $A_1, A_2, ...$ are (mutually) disjoint if
$$\bigcap_{i=1}^{\infty} A_i = \emptyset $$
Sets $A_1, A_2, ...$ are pairwise disjoint if
$$A_i \cap A_j = \emptyset \ \forall i \ne j$$
Apparently, most texts use 'disjoint' to refer to 'pairwise disjoint'. Whenever a text uses 'pairwise disjoint', we can assume 'disjoint' refers to 'mutually disjoint'.
I think it's the same as 'pairwise distinct' and 'distinct'

Some stuff on Math SE/meta
Do Kolmogorov's axioms really need only disjointness rather than pairwise disjointness?
http://meta.math.stackexchange.com/questions/21560/should-these-be-simply-disjoint-instead-of-pairwise-disjoint
Are pairwise mutually exclusive events the same as mutually exclusive events?
