Axiom:Axiom of Dependent Choice

Also known as
Some sources call this the Axiom of Dependent Choices, reflecting the infinitely many choices made.

This axiom can be abbreviated ADC or simply DC.

Also see

 * This axiom is a weaker form of the axiom of choice, as shown in Axiom of Choice Implies Axiom of Dependent Choice.


 * This axiom is also a stronger form of the axiom of countable choice, as shown in Axiom of Dependent Choice Implies Axiom of Countable Choice.


 * Dependent Choice (Fixed First Element)‎ shows that it's possible to choose any element of the set to be the first element of the sequence.