Exercise about the axiom of choice
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
14496
Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?
85769
Do you need the Axiom of Choice to accept Cantor's Diagonal Proof?
55564
Can the union axiom be weakened?
58631
Continuity and the Axiom of Choice
87451
Construction of matrices under ZFC axioms
153424
Proof of "continuity from above" and "continuity from below" from the axioms of probability
43503
Bases of complex vector spaces and the axiom of choice
118189
Proving the pairing axiom from the rest of ZF
115675
Strange consequences of Axiom of Choice in Zermelo set theory
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
155207
Confusion regarding one formulation of the Axiom of Choice.
94295
Pigeonhole-principle with two choices
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
950
Doubts on the axiom of union?
140868
Axiomatization of $\mathbb{Z}$ via well-ordering of positives.