Does every iterative definition (or at least the one describe in the details) require the use of the Axiom of Choice?
34674
Does the proof of Bolzano-Weierstrass theorem require axiom of choice?
102202
The smallest infinity and the axiom of choice
50506
What concept does an open set axiomatise?
78228
Hausdorff Maximal Principle and Axiom of Choice
25567
Is there any significance in the order in which group axioms are presented?
66636
Problems with introducing ordered pairs axiomatically
9493
While proving a universal quantification, we begin by "Let ... in ..." or "Arbitrary choose ..."?
78148
Why does the infinite prisoners and hats puzzle require the axiom of choice?
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
84485
What is the purpose of the Axiom of regularity/foundation?
19924
Uncountable ordinals without power set axiom
21374
What is exactly the difference between a definition and an axiom?
139992
Is power-associativity finitely axiomatizable?
35123
How do the separation axioms follow from the replacement axioms?
83757
Is the following equivalent to the axiom of choice?
93040
$f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki