Definition:Minimally Inductive Set/Definition 3

Definition
The minimal infinite successor set $\omega$ is defined as:


 * $\omega := \set {x \in \On: \paren {x \cup \set x} \subseteq K_I}$

where:
 * $K_I$ is the class of all non-limit ordinals
 * $\On$ is the class of all ordinals.

Also see

 * Definition:Von Neumann Construction of Natural Numbers