Gödel operation


In mathematical set theory, a set of Gödel operations is a finite collection of operations on sets that can be used to construct the constructible sets from ordinals. introduced the original set of 8 Gödel operations ?1,...,?8 under the name fundamental operations. Other authors sometimes use a slightly different set of about 8 to 10 operations, usually denoted G1, G2,...

Definition

used the following eight operations as a set of Gödel operations :
The second expression in each line gives Gödel's definition in his original notation, where the dot means intersection, V is the universe, E is the membership relation, and so on.
uses the following set of 10 Gödel operations.

Properties

Gödel's normal form theorem states that if φ is a formula with all quantifiers bounded, then the function