Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 19 / 5 / i / a

The valuation of a forcing name is defined recursively byThe recursion is on forcing name rank. Only pairs with an active condition in $H$ contribute elements, and their first coordinates are evaluated in the same filter. Thus a name is a ground-model set, while its value is a set in the generic extension.