Let $2\leq n \leq \omega$ and $F$ be a set of size $\leq n$ . Let $\mathbb{P}$ be a poset and $Q \subseteq \mathbb{P}$ an $n$-linked subset.
Questions: if $\dot{a} $ is a name for a menber of $\mathbb{P}$ ( that is, $\Vdash \dot{a} \in F)$ then there is a $c\in F$ such that $p \nVdash \dot{a}\neq c$ for all $p\in Q?$
reasons for the absurd. suppose that for all $c\in F$ there is a $p_c\in Q$ such that $p_c\Vdash\dot{a}=c$, the fact that $Q$ is $n$-linked you get a contradiction.(You'll find a forcing condition $\dot{a}\notin F$).