Axiom Schema of Separation

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:axiom_schema
gptkbp:alsoKnownAs	gptkb:Axiom_Schema_of_Subsets gptkb:Subset_Axiom_Schema
gptkbp:category	axiom of set theory
gptkbp:expressedIn	∀A ∀φ ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x))
gptkbp:field	gptkb:set_theory
gptkbp:introduced	gptkb:Ernst_Zermelo
gptkbp:introducedIn	1908
gptkbp:language	gptkb:first-order_logic
gptkbp:partOf	gptkb:Zermelo–Fraenkel_set_theory
gptkbp:prevention	gptkb:Russell's_paradox
gptkbp:purpose	restricts set formation to avoid paradoxes
gptkbp:relatedTo	gptkb:Axiom_Schema_of_Replacement gptkb:Axiom_of_Comprehension gptkb:Axiom_of_Specification
gptkbp:replacedBy	unrestricted comprehension
gptkbp:state	for any set and any property, there is a subset of the set containing exactly those elements that satisfy the property
gptkbp:usedIn	gptkb:Zermelo–Fraenkel_set_theory gptkb:ZFC gptkb:Zermelo_set_theory
gptkbp:bfsParent	gptkb:Axiom_of_Separation
gptkbp:bfsLayer	6
https://www.w3.org/2000/01/rdf-schema#label	Axiom Schema of Separation