Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
set theory principle |
| gptkbp:controversy |
non-constructive existence
|
| gptkbp:equivalentTo |
gptkb:Well-ordering_theorem
gptkb:Zorn’s_Lemma |
| gptkbp:field |
gptkb:mathematics
gptkb:set_theory |
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
1904 |
| https://www.w3.org/2000/01/rdf-schema#label |
Zermelo’s Axiom of Choice
|
| gptkbp:namedAfter |
gptkb:Ernst_Zermelo
|
| gptkbp:relatedTo |
gptkb:axiom_of_countable_choice
gptkb:axiom_of_dependent_choice |
| gptkbp:statedIn |
Given any collection of nonempty sets, there exists a choice function selecting one element from each set.
|
| gptkbp:statusInNBG |
gptkb:Titan
|
| gptkbp:statusInZF |
independent
|
| gptkbp:statusInZFC |
gptkb:Titan
|
| gptkbp:symbol |
gptkb:AC
|
| gptkbp:usedIn |
proof of Hahn–Banach theorem
proof of Tychonoff’s theorem proof of every vector space has a basis |
| gptkbp:bfsParent |
gptkb:Gregory_H._Moore
|
| gptkbp:bfsLayer |
7
|