= Solution
\b[A <set> $G\subseteq\mathbb P$ is a <generic filter> over $M$ if it is nonempty, is closed towards weaker conditions, is directed towards stronger common extensions, and meets every dense <subset> $D\subseteq\mathbb P$ belonging to $M$.] Density means that every condition has a stronger extension in $D$. Genericity is relative to $M$, not to every <dense subset of a forcing order> in the ambient universe. Under the printed weaker-first convention in Question 5, closure is towards smaller conditions and directedness is towards larger ones; in the standard stronger-first notation these inequalities reverse.
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