Definition 1. A choice function on a set $X$ is a function on $X$ such that
\[\forall A \in X : f(A) \in A.\]Axiom 1. Axiom of Choice ($\AC$). Every set has a choice function.
Proposition 1. $\AC$ is independent of $\ZF$.
$\ZF + \AC$ is denoted by $\ZFC$.
References
- [1]
- Wikipedia contributors. Axiom of choice. Wikipedia, The Free Encyclopedia.
- [2]
- Thomas Jech. Set Theory. 3rd Millennium ed, rev. and expanded. Springer, 2002. p. 46.