Is it possible create a not measurable set absence of axiom of choice?
14496
Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?
129227
An example of neither open nor closed set
19924
Uncountable ordinals without power set axiom
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
27899
Can we prove the existence of $A\cup B$ without the union axiom?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
132692
Nonempty set mapped to $\emptyset$ and vice-versa
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
47697
Russell's paradox: a set cannot contain its own powerset
82236
Extension of the Lebesgue measurable sets
78290
Countable axiom of choice: why you can't prove it from just ZF
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
74440
How does the axiom of regularity forbid self containing sets?
84378
Does axiom of foundation/regularity protect against Russell-like paradoxes?