Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:category |
gptkb:logic
|
| gptkbp:field |
gptkb:Set_theory
|
| gptkbp:firstPublished |
1908
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Extensionality
|
| gptkbp:importantFor |
Foundation of modern set theory
|
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:relatedConcept |
gptkb:Axiom_of_Pairing
gptkb:Axiom_of_Regularity gptkb:Axiom_of_Union |
| gptkbp:state |
Two sets are equal if and only if they have the same elements
|
| gptkbp:symbol |
∀A ∀B [∀x (x ∈ A ↔ x ∈ B) → A = B]
|
| gptkbp:usedIn |
gptkb:ZF
gptkb:ZFC gptkb:Von_Neumann–Bernays–Gödel_set_theory |
| gptkbp:bfsParent |
gptkb:set_theory
|
| gptkbp:bfsLayer |
4
|