query: Every set with more than point admits a permutation with no fixed point and the Axiom of Choice
positive_passages.docid: 37331
positive_passages.text: Prove that every set with more than one element has a permutation without fixed points
negative_passages.docid: 84394
negative_passages.text: Choice function for a collection of nonempty subsets of $\{0,1\}^\omega$
negative_passages.docid: 45878
negative_passages.text: Elementary Set Theory: Ordinals, Well Orderings and Isomorphisms
negative_passages.docid: 139992
negative_passages.text: Is power-associativity finitely axiomatizable?
negative_passages.docid: 115675
negative_passages.text: Strange consequences of Axiom of Choice in Zermelo set theory
negative_passages.docid: 41937
negative_passages.text: Can one construct a non-measurable set without Axiom of choice?
negative_passages.docid: 52451
negative_passages.text: Ordered Triples and Set Theory
negative_passages.docid: 114770
negative_passages.text: Proof that a perfect set is uncountable
negative_passages.docid: 13779
negative_passages.text: Canonical copies of sets
negative_passages.docid: 109054
negative_passages.text: Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
negative_passages.docid: 90685
negative_passages.text: The composition of non-linear entire functions with no fixed points has infinitely many fixed points.
negative_passages.docid: 92249
negative_passages.text: Every finite set contains its supremum: proof improvement.
negative_passages.docid: 19924
negative_passages.text: Uncountable ordinals without power set axiom
negative_passages.docid: 156161
negative_passages.text: Banach-Tarski theorem without axiom of choice
negative_passages.docid: 65308
negative_passages.text: Axiom of Choice: Family of non-empty sets mutually disjoint or not?
negative_passages.docid: 108922
negative_passages.text: Cardinality and infinite sets: naturals, integers, rationals, bijections
negative_passages.docid: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice