Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:alsoKnownAs |
gptkb:Axiom_schema_of_separation
gptkb:Axiom_schema_of_specification Subset axiom |
| gptkbp:category |
gptkb:logic
gptkb:Set_theory |
| gptkbp:distinctFrom |
gptkb:Axiom_of_unrestricted_comprehension
|
| gptkbp:expressedIn |
∀A ∀φ ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x))
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Subsets
|
| gptkbp:implies |
Existence of subsets defined by properties
|
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:prevention |
gptkb:Russell's_paradox
|
| gptkbp:prohibits |
gptkb:Comprehension_principle
|
| gptkbp:purpose |
To ensure the existence of subsets defined by a property
|
| gptkbp:sentence |
For any set and any property, there is a subset of the set containing exactly those elements that satisfy the property.
|
| gptkbp:statedIn |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:usedIn |
gptkb:Axiomatic_set_theory
|
| gptkbp:bfsParent |
gptkb:Axiom_of_Separation
|
| gptkbp:bfsLayer |
6
|