query: Axiom of choice condition.
positive_passages.docid: 65308
positive_passages.text: Axiom of Choice: Family of non-empty sets mutually disjoint or not?
negative_passages.docid: 142219
negative_passages.text: Does the splitting lemma hold without the axiom of choice?
negative_passages.docid: 77546
negative_passages.text: Does a "backwards" choice function imply the Axiom of Choice?
negative_passages.docid: 12539
negative_passages.text: Set Theory: Equivalency of Axiom of Choice and Choice Function
negative_passages.docid: 78148
negative_passages.text: Why does the infinite prisoners and hats puzzle require the axiom of choice?
negative_passages.docid: 9158
negative_passages.text: Proving that a propositional theory of any cardinality has an independent set of axioms
negative_passages.docid: 121060
negative_passages.text: ¿Can you help me with axiom of regularity?
negative_passages.docid: 98580
negative_passages.text: Lebesgue-measurable sets requiring the Axiom of Choice to construct
negative_passages.docid: 152272
negative_passages.text: Can you explain the "Axiom of choice" in simple terms?
negative_passages.docid: 9493
negative_passages.text: While proving a universal quantification, we begin by "Let ... in ..." or "Arbitrary choose ..."?
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: 13661
negative_passages.text: Axiom of Regularity allows for this set be an element of itself
negative_passages.docid: 72185
negative_passages.text: The negation of a limit condition, Spivak style.
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF
negative_passages.docid: 115675
negative_passages.text: Strange consequences of Axiom of Choice in Zermelo set theory
negative_passages.docid: 58631
negative_passages.text: Continuity and the Axiom of Choice
negative_passages.docid: 950
negative_passages.text: Doubts on the axiom of union?