New posts in Axiom Of Choice

In ZF, if injection from A to B doesn't exist, then does surjection from A to B exist?

In ZF, does the ring of continuous functions $C([0,1], \mathbb{R})$ have prime ideals which is not maximal?

Is there an object such that its unique existence follows from choice axiom, while its existence cannot be proven without choice axiom?

Prove that the axiom of choice is necessary in order to prove something else.

Is Fodor's Lemma necessary for the $\omega_1$ train station puzzle?

There is a $\Sigma^1_1$ universal set and this is not Borel. Where did we use the axiom of choice?

Implicit $AC$ in Munkres' Proof? (Completely Regular Spaces)

Simple Failings of Axiom of Choice in Top

Is it required to use choice principles to prove that any linearly independent set can be extended to a basis?

"Indexed" version of compactness and Axiom of Choice