Definition:Minimal Infinite Successor Set/Definition 1

Definition

Let $S$ be an infinite successor set.

The minimal infinite successor set $\omega$ is the infinite successor set given by:

$\omega := \displaystyle \bigcap \set {S' \subseteq S: \text{$S'$is an infinite successor set} }$

that is, $\omega$ is the intersection of every infinite successor set which is a subset of $S$.

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