# Category:Definitions/Minimal Infinite Successor Set

This category contains definitions related to Minimal Infinite Successor Set.
Related results can be found in Category:Minimal Infinite Successor Set.

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 $S$.

## Pages in category "Definitions/Minimal Infinite Successor Set"

The following 7 pages are in this category, out of 7 total.