Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:alsoKnownAs |
gptkb:Axiom_of_Separation
gptkb:Subset_Axiom |
| gptkbp:compatibleWith |
gptkb:Naive_set_theory
|
| gptkbp:expressedIn |
∀A ∀P ∃B ∀x (x ∈ B ↔ x ∈ A ∧ P(x))
|
| gptkbp:field |
gptkb:Set_theory
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Specification
|
| gptkbp:prevention |
Formation of sets by unrestricted comprehension
|
| gptkbp:purpose |
To avoid Russell's paradox
|
| gptkbp:relatedTo |
gptkb:Russell's_paradox
|
| gptkbp:replacedBy |
gptkb:Axiom_schema_of_unrestricted_comprehension
|
| gptkbp:state |
For any set and any property, there is a subset containing exactly those elements of the set that satisfy the property.
|
| gptkbp:statedIn |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:type |
gptkb:Axiom_schema
|
| gptkbp:usedIn |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Zermelo_set_theory |
| gptkbp:bfsParent |
gptkb:Axiom_Schema_of_Separation
|
| gptkbp:bfsLayer |
7
|