query: Axiom of choice equivalence problem.
positive_passages.docid: 21202
positive_passages.text: Axiom of choice is equivalent to every relation includes a function with the same domain
negative_passages.docid: 19924
negative_passages.text: Uncountable ordinals without power set axiom
negative_passages.docid: 78148
negative_passages.text: Why does the infinite prisoners and hats puzzle require the axiom of choice?
negative_passages.docid: 126870
negative_passages.text: Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]
negative_passages.docid: 3663
negative_passages.text: Finding counterexamples in elementary set theory.
negative_passages.docid: 108367
negative_passages.text: proving tautologically equivalent
negative_passages.docid: 18287
negative_passages.text: Distinction between equality, logical equivalence and biconditionality.
negative_passages.docid: 29744
negative_passages.text: Compactness and axiomatisability
negative_passages.docid: 44620
negative_passages.text: Reference for combinatorial game theory.
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: 66548
negative_passages.text: proving topological equivalence
negative_passages.docid: 68032
negative_passages.text: A Representation Theory Problem in Putnam Competition
negative_passages.docid: 131889
negative_passages.text: Axiom of choice and calculus
negative_passages.docid: 41365
negative_passages.text: Choice function for collection of arbitrary finite sets. AC required?
negative_passages.docid: 139866
negative_passages.text: What are the Axiom of Choice and Axiom of Determinacy?
negative_passages.docid: 78228
negative_passages.text: Hausdorff Maximal Principle and Axiom of Choice
negative_passages.docid: 132287
negative_passages.text: Axiom of Choice and Right Inverse