Let 𝟙 be a Forcing Partial Order. We define the -names by recursion:

Furthermore, fix some and define by -recursion:

We may write for .

Interpretation

If then guarantees that the set named by is in the set named by .

Remark

When 𝟙 then this is the Von Neumann Hierarchy.

Lemma

is Absolute for Transitive Models of a Sufficiently Strong . In other words, there is an Absolute Function Class such that

Furthermore, is also Absolute for Transitive Models of a Sufficiently Strong .