Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 121 / 3 / iv / a

A cardinal-preserving forcing over $M$ leaves every ground-model cardinal number a cardinal in every generic extension. In the present notation, for every $M$-generic filter $G$ and every ordinal $\kappa \in M$,Set forcing preserves ordinals, and an old bijection witnessing that an ordinal is not a cardinal remains available. Thus this condition also means that the two models have exactly the same cardinals. Cardinality here is computed inside the respective models, not from their external sizes.