question about the axiom of choice
20252
The Axiom of Choice and the Cartesian Product.
118573
Why is the Axiom of Infinity necessary?
115675
Strange consequences of Axiom of Choice in Zermelo set theory
48615
Does the assertion that every two cardinalities are comparable imply the axiom of choice?
144899
Do We Need the Axiom of Choice for Finite Sets?
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
139992
Is power-associativity finitely axiomatizable?
153935
A weaker Axiom of Infinity?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
147908
Why use the biconditional in the Axiom of Extensionality
105815
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
104771
Dedekind's cut and axioms
120311
Equivalence of Axiom of Regularity
14496
Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?