A <forcing name> for $\mathbb P$ is a set of ordered pairs $(\sigma,p)$ where $p\in P$ and $\sigma$ is itself a <forcing name>. This recursive definition is made well-founded by assigning the <forcing name rank> $\sup\{\operatorname{nrk}(\sigma)+1:(\sigma,p)\in\tau\}$. Names over the ground model are those names belonging to $M$; conditions remain ground-model objects. A name describes which recursively interpreted elements are activated by the <generic filter>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 19 / 4 / i / a / Solution

 Solution (source code)