Perhaps the word is 'product'? I am thinking along the lines that the cartesian product of the set of all Individuals and the set of all Events is the set of all possible Occurrences. Unfortunately, 'intersection' is quite a good word if we are thinking in natural language, and 'product' is not - not unless you are already thinking in terms of a mathematical vocabulary.
Hmmm, thinking about the mathematical definition of "product", it would seem to me that the "product" would be some sort of representation of all *possible* combinations of unique events and unique individuals; rather than just the tiny, tiny, tiny subset of those that ever existed, and the even tinier, tinier, tinier susbset that have actually been documented.
In database-speak, an Occurrence is simply a many-to-many join between Events and Individuals, with a few additional properties.
...which is what I *used* to use the word "intersection" for.
It reminds me of the time when, as a young undergrad, I was informed that I could no longer use the word "significant" in the sense of "important"....
Aloha, Rich