Uses of Axiom of Choice
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
106670
Existence of vector space complement and axiom of choice
77546
Does a "backwards" choice function imply the Axiom of Choice?
132287
Axiom of Choice and Right Inverse
156161
Banach-Tarski theorem without axiom of choice
56191
How to demystify the axioms of propositional logic?
62936
Proving equivalencies of two versions of the Axiom of Choice
141299
Alternative set theories
118189
Proving the pairing axiom from the rest of ZF
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
105815
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
31389
consistency of ZF\{Power Set axiom}
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
29755
Power set equivalency of Axiom of Choice
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
49276
Why don't you need the Axiom of Choice when constructing the "inverse" of an injection?
149277
Does well-ordering of the proper class of cardinal numbers imply choice?