The forcing order $\mathbb P$ has the <chain condition for forcing> at $\kappa$ when every <antichain in a forcing order> has cardinality below $\kappa$:
$$
\boxed{\forall A\subseteq\mathbb P\ \bigl(A\text{ an antichain}\Longrightarrow |A|<\kappa\bigr).}
$$
When this assertion is evaluated inside $M$, both the quantified subsets and their <cardinalities> are those of $M$.

Solution

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

 Solution

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