Definition of the reals and basic proofs are independent of the axiom of choice?
58631
Continuity and the Axiom of Choice
83714
$A \in B$ vs. $A \subset B$ for proofs
84562
Proof using only field axioms
85769
Do you need the Axiom of Choice to accept Cantor's Diagonal Proof?
141814
Proofs using theorems instead of axioms
152272
Can you explain the "Axiom of choice" in simple terms?
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
29755
Power set equivalency of Axiom of Choice
142026
Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
62936
Proving equivalencies of two versions of the Axiom of Choice
50506
What concept does an open set axiomatise?
102202
The smallest infinity and 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?
27899
Can we prove the existence of $A\cup B$ without the union axiom?
88566
Is denying "Paradoxical Partitioning" equivalent to accepting the Axiom of Choice?
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
21202
Axiom of choice is equivalent to every relation includes a function with the same domain