Does the Axiom schema of Replacement imply the Axiom of Infinity?
118573
Why is the Axiom of Infinity necessary?
7214
Does linear ordering need the Axiom of Choice?
157490
Statements equivalent to the Axiom of Choice
155207
Confusion regarding one formulation of the Axiom of Choice.
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
16796
Zermelo-Fraenkel set theory and Hilbert's axioms for geometry
108533
Is there any formula of monadic second-order logic that is only satisfied by an infinite set?
88566
Is denying "Paradoxical Partitioning" equivalent to accepting the Axiom of Choice?
135222
What are the consequences if Axiom of Infinity is negated?
31212
The existence of the empty set is an axiom of ZFC or not?
139678
Advantage of accepting the axiom of choice
121847
Don't we need the axiom of choice to choose from a non-empty set?
7865
Complete Newbie: Axiom of Foundation Exercise
85769
Do you need the Axiom of Choice to accept Cantor's Diagonal Proof?
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
58631
Continuity and the Axiom of Choice
29755
Power set equivalency of Axiom of Choice