axiom of countable choice

The Axiom of Countable Choice (CC) is a weak form of the Axiom of ChoiceMathworldPlanetmath ( It states that every countable set of nonempty sets has a choice function.

(that is, the Zermelo-Fraenkel axiomsMathworldPlanetmath together with the Axiom of Countable Choice) suffices to prove that the union of countably many countable sets is countableMathworldPlanetmath. It also suffices to prove that every infinite setMathworldPlanetmath has a countably infiniteMathworldPlanetmath subset, and that a set X is infinite if and only if there is a bijection between X and a proper subsetMathworldPlanetmathPlanetmath of X.

Title axiom of countable choice
Canonical name AxiomOfCountableChoice
Date of creation 2013-03-22 14:46:23
Last modified on 2013-03-22 14:46:23
Owner yark (2760)
Last modified by yark (2760)
Numerical id 14
Author yark (2760)
Entry type Definition
Classification msc 03E25
Synonym countable axiom of choice
Synonym countable AC
Defines countable choice