Definition:Minimally Inductive Set/Definition 1

Definition
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 $S$.

Also see

 * Equivalence of Definitions of Minimally Inductive Set


 * Definition:Von Neumann Construction of Natural Numbers