Axiom schema of specification
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
axiom schema
|
| gptkbp:alsoKnownAs |
gptkb:axiom_schema_of_separation
gptkb:axiom_schema_of_restricted_comprehension |
| gptkbp:category |
gptkb:axiom_of_Zermelo–Fraenkel_set_theory
|
| gptkbp:contrastsWith |
axiom schema of unrestricted comprehension
|
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:formalStatement |
For any set A and property φ(x), there exists a set B such that x ∈ B if and only if x ∈ A and φ(x) holds.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom schema of specification
|
| gptkbp:implies |
all subsets of a set are sets
|
| gptkbp:introduced |
gptkb:Ernst_Zermelo
|
| gptkbp:introducedIn |
1908
|
| gptkbp:prevention |
formation of sets by arbitrary properties
|
| gptkbp:purpose |
to avoid Russell's paradox
|
| gptkbp:state |
for any set and any property, there is a subset containing exactly those elements of the set that satisfy the property
|
| gptkbp:usedIn |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:bfsParent |
gptkb:Axiom_of_Replacement
|
| gptkbp:bfsLayer |
5
|