A class in material set theory is big if for any set there exists a set such that .
Consider a class as a formula with a free variable ; intuitively is the collection of all sets such that is true. Then, in the metalanguage, is big (i.e., the formula exhibits a big class) if
\phi(X) \implies (\exists Y)(\phi(Y) \wedge (X\in Y))
Examples and properties
Gödel’s constructible universe is a transitive big class.
Revised on January 8, 2011 05:44:15
by Toby Bartels