A set $G\subseteq\mathbb P$ is a filter when it is upward closed toward weaker conditions and downward directed: if $p\in G$ and $p\leq q$, then $q\in G$, while any $p,q\in G$ have some $r\in G$ with $r\leq p,q$. It is a <generic filter> over $M$ when
$$
\boxed{G\cap D\ne\varnothing\quad\text{for every dense }D\subseteq\mathbb P\text{ with }D\in M.}
$$

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-121/3/i/b/solution