TITLE: Mutually generics
QUESTION [7 upvotes]: Given posets $P,Q\in M$, I would like to know under what circumstances there are mutually generic filters $G\subseteq P$ and $H\subseteq Q$ (generic over $M$). Also, what are the characterizations of mutual genericity? And finally, what can we say about the relation between $M[G]$ and $M[H]$ in that case?
I have a slight difficulty finding references to the notion and properties of mutual genericity (whatever they are).

REPLY [8 votes]: Another fact to add to Joel's list, one which I found surprising when I first came across it, is that adding a single Cohen real adds a perfect set of reals such that any finitely many are mutually generic over each other. To see this simply consider the trace of a Cohen real on the members of an almost disjoint family and use the theorem Joel quotes about products.