Can this proof be written without invoking the Axiom of Choice?
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
139678
Advantage of accepting the axiom of choice
122324
Is there a proof of Gödel's Incompleteness Theorem without self-referential statements?
950
Doubts on the axiom of union?
157490
Statements equivalent to the Axiom of Choice
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?
151356
Need Hints Prove "$((\neg \alpha \to \alpha) \to \alpha) $" Using Axiom 1,2,3 and MP and deduction theorem
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
65371
Does $2^X \cong 2^Y$ imply $X \cong Y$ without assuming the axiom of choice?
80019
$\varepsilon$-number countability without choice
41318
Can every proof by contradiction also be shown without contradiction?
132287
Axiom of Choice and Right Inverse
141814
Proofs using theorems instead of axioms
32009
Prove $\;\big((p\rightarrow q) \lor (p \rightarrow r)\big) \rightarrow (q\lor r)\equiv p \lor q \lor r$ without use of a truth table.
88566
Is denying "Paradoxical Partitioning" equivalent to accepting the Axiom of Choice?
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)