# axiom of countable choice

The Axiom of Countable Choice (CC) is a weak form of the Axiom of Choice (http://planetmath.org/AxiomOfChoice). It states that every countable set of nonempty sets has a choice function.

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

Title axiom of countable choice AxiomOfCountableChoice 2013-03-22 14:46:23 2013-03-22 14:46:23 yark (2760) yark (2760) 14 yark (2760) Definition msc 03E25 countable axiom of choice countable AC countable choice