Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 19 / 5 / i / b / Solution

The forcing truth lemma says that for a formula $\phi$ and ground-model forcing names ${\tau }_1,\dots ,{\tau }_n$,The forcing relation is the ground-model relation furnished by the forcing theorem. The witnessing condition must belong to the particular generic filter, not merely to the forcing order.