Definition:Choice Function/Chosen Element
Let $\mathbb S$ be a set of sets such that:
- $\forall S \in \mathbb S: S \ne \O$
that is, none of the sets in $\mathbb S$ may be empty.
Let $f: \mathbb S \to \ds \bigcup \mathbb S$ be a choice function on $\mathbb S$.
For a given $S \in \mathbb S$, the image $\map f S$ of $S$ is referred to as the $f$-chosen element of $S$.
- Results about choice functions can be found here.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 4$ Well ordering and choice