KnowraAxiom of choiceLinked fromLinked fromThe 48 pages that link to Axiom of choice, each with the reason it gives.All 48Broader topic 2Related 32Narrower topic 5Compared with 9Constructive mathematicsCompared with: Its unrestricted form can assert choices without supplying an explicit selection procedure.Axiom of pairingCompared with: It concerns simultaneous selections, not the existence of a set with two specified members.Axiom of unionCompared with: Union collects the family’s elements but does not choose one element from each member.UltrafilterCompared with: The ultrafilter lemma is weaker than the full axiom of choice, despite common proofs using choice.Axiom of determinacyCompared with: The two principles cannot both hold in the usual set-theoretic setting.Boolean prime ideal theoremCompared with: The theorem follows from choice, but choice is strictly stronger.Axiom of regularityCompared with: It is often discussed alongside regularity, but addresses selection rather than membership structure.Schröder–Bernstein theoremCompared with: The theorem itself needs no choice, unlike some broader results about comparing arbitrary cardinalities.Rasiowa–Sikorski lemmaCompared with: The lemma gives a structured countable construction rather than unrestricted simultaneous choices.