[FOM] Diagonal intersection

[Thomas Forster]

The diagonal intersection of a family $C_\alpha: \alpha \in I$ of sets
is $\{\beta: (\forall \gamma < \beta)(\beta \in C_\gamma)\}$.

I've know the definition for years (a normal filter on a measurable
cardinal is closed under diagonal intersections for example) but i've
never known who first isolated the concept or what purpose of theirs was
served by so doing.  Harold Simmons suggested to me that it might come
from projective set theory but i've never heard it in that connection. I
was reminded of it the other day when preparing myself for the reading
group we have here in Canterbury on Countable ordinals (The family of
clubsets of countable ordinals is closed under diagonal intersection so it
clearly has something to do with getting rapidly growing functions form
the second number class into itself) but i've never heard it explicitly
mentioned in that connection either.

     Can listmembers enlighten me about who invented it, where, when and 
why?

              tf


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