Definition:Minimal Infinite Successor Set/Definition 3

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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.


Sources