query: Does this proof require the axiom of choice?
positive_passages.docid: 142219
positive_passages.text: Does the splitting lemma hold without the axiom of choice?
negative_passages.docid: 78148
negative_passages.text: Why does the infinite prisoners and hats puzzle require the axiom of choice?
negative_passages.docid: 93040
negative_passages.text: $f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
negative_passages.docid: 73526
negative_passages.text: The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
negative_passages.docid: 48615
negative_passages.text: Does the assertion that every two cardinalities are comparable imply the axiom of choice?
negative_passages.docid: 157490
negative_passages.text: Statements equivalent to the Axiom of Choice
negative_passages.docid: 118573
negative_passages.text: Why is the Axiom of Infinity necessary?
negative_passages.docid: 33563
negative_passages.text: Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
negative_passages.docid: 77548
negative_passages.text: Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
negative_passages.docid: 21202
negative_passages.text: Axiom of choice is equivalent to every relation includes a function with the same domain
negative_passages.docid: 31509
negative_passages.text: Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
negative_passages.docid: 50506
negative_passages.text: What concept does an open set axiomatise?
negative_passages.docid: 19414
negative_passages.text: Uncountable subset with uncountable complement, without the Axiom of Choice
negative_passages.docid: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice
negative_passages.docid: 950
negative_passages.text: Doubts on the axiom of union?
negative_passages.docid: 106670
negative_passages.text: Existence of vector space complement and axiom of choice
negative_passages.docid: 65308
negative_passages.text: Axiom of Choice: Family of non-empty sets mutually disjoint or not?