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

The forcing order $\mathbb{P}$ has the chain condition for forcing at $\kappa$ when every antichain in a forcing order has cardinality below $\kappa$:When this assertion is evaluated inside $M$, both the quantified subsets and their cardinalities are those of $M$.