## § Godel operations

• 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.