query: Does this choice require Axiom of Choice?
positive_passages.docid: 27025
positive_passages.text: How do I choose an element from a non-empty set?
negative_passages.docid: 82169
negative_passages.text: Why does a partially ordered set need to be reflexive?
negative_passages.docid: 118573
negative_passages.text: Why is the Axiom of Infinity necessary?
negative_passages.docid: 142219
negative_passages.text: Does the splitting lemma hold without the axiom of choice?
negative_passages.docid: 130865
negative_passages.text: Why is the axiom of choice separated from the other axioms?
negative_passages.docid: 153935
negative_passages.text: A weaker Axiom of Infinity?
negative_passages.docid: 53025
negative_passages.text: Why the need of Axiom of Countable Choice?
negative_passages.docid: 149277
negative_passages.text: Does well-ordering of the proper class of cardinal numbers imply choice?
negative_passages.docid: 142840
negative_passages.text: Open axioms of equality
negative_passages.docid: 55564
negative_passages.text: Can the union axiom be weakened?
negative_passages.docid: 3902
negative_passages.text: Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
negative_passages.docid: 134416
negative_passages.text: have to / must / should / ought as applied to inanimate objects
negative_passages.docid: 84378
negative_passages.text: Does axiom of foundation/regularity protect against Russell-like paradoxes?
negative_passages.docid: 12449
negative_passages.text: How to formulate continuum hypothesis without the axiom of choice?
negative_passages.docid: 139678
negative_passages.text: Advantage of accepting the axiom of choice
negative_passages.docid: 59820
negative_passages.text: ZF Extensionality axiom
negative_passages.docid: 132046
negative_passages.text: Looking for Cantor's original proof of the Cantor-Bernstein theorem that relies on the axiom of choice?