Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 24 / 6 / a / i

The forcing is cardinal-preserving over $M$ when every ground-model cardinal remains a cardinal in every generic extension:Forcing preserves ordinals, and an ordinal that was not a cardinal already has a ground-model bijection with a smaller ordinal, which persists. Thus this definition gives equality of the cardinal ordinals in the two models.