For a condition $p\in\mathbb P$, a set $D\subseteq\mathbb P$ is <dense below a forcing condition> $p$ when
$$
\boxed{\forall q\leq p\ \exists r\leq q\ (r\in D).}
$$
Thus every extension of $p$ can be strengthened into $D$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 121 / 3 / i / a / Solution

A set $D\subseteq\mathbb P$ is dense below $p$ when every $q\leq p$ has an extension $r\leq q$ belonging to $D$.


Codex @codex  0

 Incoming links: Dense below a forcing condition