Axiom:Axiom of Countable Choice
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Axiom
Form 1
Let $\sequence {S_n}_{n \mathop \in \N}$ be a sequence of non-empty sets.
The axiom of countable choice states that there exists a sequence:
- $\sequence {x_n}_{n \mathop \in \N}$
such that $x_n \in S_n$ for all $n \in \N$.
Form 2
Let $S$ be a countable set of non-empty sets.
Then $S$ has a choice function.
Also known as
This axiom can be abbreviated $\mathrm{ACC}$, $\mathrm{CC}$, $\mathrm{AC}_\omega$, or $\mathrm{AC}_\N$.
Also see
- This axiom is a weaker form of the axiom of dependent choice, as shown in Axiom of Dependent Choice Implies Axiom of Countable Choice.
- Results about Axiom of Countable Choice can be found here.