Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
axiom schema
|
| gptkbp:alsoKnownAs |
gptkb:Axiom_Schema_of_Subsets
gptkb:Subset_Axiom_Schema |
| gptkbp:category |
axiom of set theory
|
| gptkbp:expressedIn |
∀A ∀φ ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x))
|
| gptkbp:field |
gptkb:set_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom Schema of Separation
|
| gptkbp:introduced |
gptkb:Ernst_Zermelo
|
| gptkbp:introducedIn |
1908
|
| gptkbp:language |
gptkb:first-order_logic
|
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:prevention |
gptkb:Russell's_paradox
|
| gptkbp:purpose |
restricts set formation to avoid paradoxes
|
| gptkbp:relatedTo |
gptkb:Axiom_Schema_of_Replacement
gptkb:Axiom_of_Comprehension gptkb:Axiom_of_Specification |
| gptkbp:replacedBy |
unrestricted comprehension
|
| gptkbp:state |
for any set and any property, there is a subset of the set containing exactly those elements that satisfy the property
|
| gptkbp:usedIn |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:ZFC gptkb:Zermelo_set_theory |
| gptkbp:bfsParent |
gptkb:Axiom_of_Separation
|
| gptkbp:bfsLayer |
6
|