Category:Definitions/Minimally Inductive Set

This category contains definitions related to the minimally inductive set.
Related results can be found in Category:Minimally Inductive Set.

Let $S$ be an inductive set.

The minimally inductive set $\omega$ is the inductive set given by:

$\ds \omega := \bigcap \set {S' \subseteq S: S' \text{ is an inductive set} }$

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