Generic filter for an atomless order is new
= Generic filter for an atomless order is new
{title2=$G\notin M$}
If a <generic filter> $G$ for an <atomless forcing order> belonged to its ground model, then the complement $\mathbb P\setminus G$ would be a dense ground-model <set>. A condition outside $G$ is already there; a condition in $G$ has two incompatible strengthenings, at least one outside its directed filter. Genericity would then require meeting the complement, a contradiction.