equivalent versions of axiom of choice
29755
Power set equivalency of Axiom of Choice
50506
What concept does an open set axiomatise?
35156
Constructing a choice function in a complete & separable metric space
134319
When induction proofs need a choice function
78290
Countable axiom of choice: why you can't prove it from just ZF
38242
Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
70262
Can the axiom of choice be used to define the real numbers?
85769
Do you need the Axiom of Choice to accept Cantor's Diagonal Proof?
58631
Continuity and the Axiom of Choice
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
103154
Is there a *simple* example of how the axiom of choice can lead to a counterintuitive result?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
132046
Looking for Cantor's original proof of the Cantor-Bernstein theorem that relies on the axiom of choice?
139678
Advantage of accepting the axiom of choice
83985
Equivalent statements to fixed-point theorem
98580
Lebesgue-measurable sets requiring the Axiom of Choice to construct