|
gptkbp:instanceOf
|
gptkb:Titan
gptkb:set_theory
|
|
gptkbp:alsoKnownAs
|
gptkb:Axiom_Schema_of_Separation
gptkb:Axiom_of_Subsets
gptkb:Subset_Axiom
|
|
gptkbp:category
|
gptkb:logic
|
|
gptkbp:expressedIn
|
gptkb:first-order_logic
|
|
gptkbp:formedBy
|
gptkb:Ernst_Zermelo
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Axiom of Separation
|
|
gptkbp:introducedIn
|
1908
|
|
gptkbp:notImplies
|
existence of universal set
|
|
gptkbp:partOf
|
gptkb:Zermelo–Fraenkel_set_theory
|
|
gptkbp:prevention
|
formation of too large sets
|
|
gptkbp:purpose
|
to avoid set-theoretic paradoxes such as Russell's paradox
|
|
gptkbp:relatedTo
|
gptkb:Axiom_of_Replacement
gptkb:Axiom_of_Comprehension
|
|
gptkbp:replacedBy
|
gptkb:Axiom_of_unrestricted_comprehension
|
|
gptkbp:schemaType
|
axiom schema
|
|
gptkbp:state
|
For any set and any property definable by a formula, there is a subset containing exactly those elements of the set that satisfy the property.
|
|
gptkbp:usedIn
|
gptkb:Zermelo_set_theory
gptkb:ZFC_set_theory
|
|
gptkbp:bfsParent
|
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Axiom_of_Replacement
gptkb:Zermelo-Fraenkel_set_theory
|
|
gptkbp:bfsLayer
|
5
|