Axiom Schema of Specification
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
axiom schema
|
| gptkbp:alsoKnownAs |
gptkb:Axiom_Schema_of_Separation
|
| gptkbp:category |
gptkb:axiom_of_set_existence
|
| gptkbp:component |
gptkb:ZFC_axioms
|
| gptkbp:expressedIn |
∀A ∀φ ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x))
|
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
1908 |
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom Schema of Specification
|
| gptkbp:prevention |
formation of too large sets
|
| gptkbp:purpose |
to avoid set-theoretic paradoxes such as Russell's paradox
|
| gptkbp:relatedTo |
gptkb:Russell's_paradox
|
| gptkbp:replacedBy |
gptkb:unrestricted_comprehension_axiom
|
| gptkbp:state |
for any set and any property, there is a subset containing exactly those elements of the set that satisfy the property
|
| gptkbp:type |
axiom schema (infinitely many axioms, one for each property φ)
|
| gptkbp:usedIn |
gptkb:Zermelo-Fraenkel_set_theory
|
| gptkbp:bfsParent |
gptkb:Axiomatic_set_theory
|
| gptkbp:bfsLayer |
7
|