maximality principle

Let S be a collectionMathworldPlanetmath of sets. If, for each chain CS, there exists an XS such that every element of C is a subset of X, then S contains a maximal elementMathworldPlanetmath. This is known as the maximality principle.

The maximality principle is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to the axiom of choiceMathworldPlanetmath.

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