Definition:Minimally Inductive Set/Definition 3

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


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

where $K_I$ is the class of all non-limit ordinals and $\operatorname{On}$ is the class of all ordinal numbers.

Also see

 * Definition:Natural Numbers as Elements of Minimal Infinite Successor Set