# maximality principle

Let $S$ be a collection of sets. If, for each chain $C\subseteq S$, there exists an $X\in S$ such that every element of $C$ is a subset of $X$, then $S$ contains a maximal element. This is known as the maximality principle.

The maximality principle is equivalent to the axiom of choice.

 Title maximality principle Canonical name MaximalityPrinciple Date of creation 2013-03-22 12:26:18 Last modified on 2013-03-22 12:26:18 Owner akrowne (2) Last modified by akrowne (2) Numerical id 9 Author akrowne (2) Entry type Theorem Classification msc 03E30 Classification msc 03E25 Synonym maximal principle Related topic ZornsLemma Related topic AxiomOfChoice Related topic WellOrderingPrinciple Related topic TukeysLemma Related topic ZermelosPostulate Related topic HaudorffsMaximumPrinciple