Definition:Minimal Infinite Successor Set/Definition 1

From ProofWiki
Jump to navigation Jump to search

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 $S$.


Also see

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


Sources