# Definition:Minimal Infinite Successor 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

• Results about the minimal infinite successor set can be found here.