A Universe of Sorts

A finite collection of operations that is used to create all constructible sets from ordinals.
Recall $V$ , the von neumann universe, which we build by iterating powersets starting from $\emptyset$ . That is, $f(V) = \mathcal P(V) \cup \mathcal P (\mathcal P(V))$
We construct $L$ sort of like $V$ , but we build it by not taking $P(V)$ fully, but only taking subsets that are carved out by using subsets via first order formulas used to filter the previous stage.
This makes sure that the resulting sets are independent of the peculiarities of the surrounding model, by sticking to FOL filtered formulas.

§ Godel Operations