$|A^2|=|A|$ for every infinite $A$ iff Axiom of Choice holds.
4912
Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
78228
Hausdorff Maximal Principle and Axiom of Choice
79778
$\kappa\cdot\kappa= \kappa,$ for infinite cardinals
102202
The smallest infinity and the axiom of choice
100839
If two continuous functions are equal almost everywhere on $[a,b]$, then they are equal everywhere on $[a,b]$
81682
Proving the algebraic set corresponding to a polynomial is infinite.
29755
Power set equivalency of Axiom of Choice
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
27899
Can we prove the existence of $A\cup B$ without the union axiom?
152102
Prove that for every complex $2$x$2$ matrix $A$, there exists a matrix $X$ such that $X^3=A^2$.
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
21202
Axiom of choice is equivalent to every relation includes a function with the same domain
78290
Countable axiom of choice: why you can't prove it from just ZF
119999
A property of every real polynomial.
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
139992
Is power-associativity finitely axiomatizable?
142315
How does the Axiom of Regularity apply to $A=\{1,2,3\}$?