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 disjont family.

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.