Definition:Class of All Cardinals

Definition

The class of all cardinals is the class consisting of all cardinals:

$\NN = \set {x \in \On: \exists y: x = \size y}$

where $\size y$ denotes the cardinal corresponding to the set $y$.

Also see

• Definition:Class of All Ordinals

• Results about the class of all cardinals can be found here.

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.36$