Forcing name rank
= Forcing name rank
{title2=$\operatorname{nrk}(\tau)$}
The <ordinal> assigned recursively by $\operatorname{nrk}(\tau)=\sup\{\operatorname{nrk}(\sigma)+1:(\sigma,p)\in\tau\}$. It measures dependency on subnames and justifies generic evaluation by recursion. The ordinary <rank of a set> also accounts for the coding of the <ordered pairs> and the <forcing> conditions; it need not equal this dependency <rank of a set>.