Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:set_theory
gptkb:Axiom_Schema |
| gptkbp:alsoKnownAs |
gptkb:Axiom_Schema_of_Specification
gptkb:Axiom_Schema_of_Separation gptkb:Subset_Axiom_Schema |
| gptkbp:appliesTo |
Sets
|
| gptkbp:compatibleWith |
gptkb:Proper_Classes
|
| gptkbp:expressedIn |
gptkb:First-order_logic
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
1908 |
| gptkbp:prevention |
gptkb:Russell's_Paradox
|
| gptkbp:replacedBy |
gptkb:Axiom_of_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:symbol |
∀A ∀φ ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x))
|
| gptkbp:usedIn |
gptkb:Zermelo–Fraenkel_Set_Theory
|
| gptkbp:bfsParent |
gptkb:Axiom_Schema_of_Separation
|
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom Schema of Subsets
|