Why the existence of the set of reals does not require axiom of choice?
70262
Can the axiom of choice be used to define the real numbers?
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
44522
Subsets of the reals when the Continuum Hypothesis is assumed false
49385
Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom
28629
Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?
5313
Existence of how many sets is asserted by the axiom of choice in this case?
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
70196
Is there any well-ordered uncountable set of real numbers under the original ordering?
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
50506
What concept does an open set axiomatise?
116135
A paradox related to computable reals?
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
118573
Why is the Axiom of Infinity necessary?
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence