Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical axiom
|
| gptkbp:category |
gptkb:Foundations_of_mathematics
|
| gptkbp:controversy |
Non-constructive nature
|
| gptkbp:equivalentTo |
gptkb:Well-ordering_theorem
gptkb:Zorn's_Lemma |
| gptkbp:field |
gptkb:Set_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Choice
|
| gptkbp:influenced |
Functional analysis
Modern set theory |
| gptkbp:introduced |
gptkb:Ernst_Zermelo
|
| gptkbp:introducedIn |
1904
|
| gptkbp:relatedTo |
gptkb:Continuum_hypothesis
gptkb:Axiom_of_determinacy Dependent choice |
| gptkbp:sentence |
Given any collection of nonempty sets, there exists a choice function selecting one element from each set.
|
| gptkbp:statusInZF |
Independent
|
| gptkbp:statusInZFC |
gptkb:Accepted
|
| gptkbp:symbol |
gptkb:AC
|
| gptkbp:usedIn |
gptkb:Banach–Tarski_paradox
gptkb:Tychonoff's_theorem Transfinite induction |
| gptkbp:bfsParent |
gptkb:set_theory
|
| gptkbp:bfsLayer |
4
|