query: Axiom of choice variants
positive_passages.docid: 73526
positive_passages.text: The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
negative_passages.docid: 101741
negative_passages.text: Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory?
negative_passages.docid: 139678
negative_passages.text: Advantage of accepting the axiom of choice
negative_passages.docid: 141814
negative_passages.text: Proofs using theorems instead of axioms
negative_passages.docid: 27600
negative_passages.text: Gödel's (in)completeness theorems and the axiomatization of Euclidean geometry
negative_passages.docid: 69337
negative_passages.text: Zorn's Lemma And Axiom of Choice
negative_passages.docid: 58631
negative_passages.text: Continuity and 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: 132287
negative_passages.text: Axiom of Choice and Right Inverse
negative_passages.docid: 140868
negative_passages.text: Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
negative_passages.docid: 35123
negative_passages.text: How do the separation axioms follow from the replacement axioms?
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: 3663
negative_passages.text: Finding counterexamples in elementary set theory.
negative_passages.docid: 53025
negative_passages.text: Why the need of Axiom of Countable Choice?
negative_passages.docid: 84394
negative_passages.text: Choice function for a collection of nonempty subsets of $\{0,1\}^\omega$
negative_passages.docid: 98580
negative_passages.text: Lebesgue-measurable sets requiring the Axiom of Choice to construct
negative_passages.docid: 44620
negative_passages.text: Reference for combinatorial game theory.