Does one always need some choice to show the existence of nonprincipal ultrafilters?
101453
Existence of a Boolean algebra with a unique ultrafilter in ZF
14972
Cardinality of Vitali sets: countably or uncountably infinite?
98580
Lebesgue-measurable sets requiring the Axiom of Choice to construct
156161
Banach-Tarski theorem without axiom of choice
121847
Don't we need the axiom of choice to choose from a non-empty set?
123132
Counterexample for a non-measurable function?
141366
Absolutely continuity and Lipschitz-like continuity
9330
Meaning behind Filter in Set Theory
144899
Do We Need the Axiom of Choice for Finite Sets?
98559
subtlety of self-defined function and its evaluation
17624
Axiom of Choice iff Every set has a choice function
111723
Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
34298
sequentially continuous on a non first-countable
84378
Does axiom of foundation/regularity protect against Russell-like paradoxes?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
102202
The smallest infinity and the axiom of choice
63952
Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true