Is the statement that there is a bijection $A\cong A\coprod A$ for every infinite set equivalent to the axiom of choice?
55680
The relationship of ${\frak m+m=m}$ to AC
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
139078
Infinite partition of $\mathbb N$ by infinite subsets
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
124333
A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
13924
For all infinite cardinals $\kappa, \ (\kappa \times \kappa, <_{cw}) \cong (\kappa, \in).$
62687
Proving Cardinality of Cosets in Abstract Algebra
36281
A set is infinite iff it is equivalent to a proper subset of itself
48615
Does the assertion that every two cardinalities are comparable imply the axiom of choice?
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
4912
Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$