Axiom Schema of Replacement

GPTKB entity

Predicate	Object
gptkbp:instanceOf	axiom schema
gptkbp:alsoKnownAs	gptkb:Axiom_of_Replacement
gptkbp:category	gptkb:logic axiom of set theory
gptkbp:enables	transfinite recursion construction of cumulative hierarchy
gptkbp:excludes	gptkb:Zermelo_set_theory
gptkbp:field	gptkb:set_theory
gptkbp:formedBy	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
https://www.w3.org/2000/01/rdf-schema#label	Axiom Schema of Replacement
gptkbp:includedIn	gptkb:ZFC
gptkbp:introducedIn	1922
gptkbp:relatedTo	gptkb:Axiom_of_Separation gptkb:Axiom_of_Collection
gptkbp:replacedBy	gptkb:Axiom_of_Substitution
gptkbp:requires	development of ordinal and cardinal numbers
gptkbp:state	the image of a set under any definable function is also a set
gptkbp:symbol	∀A ∀F ∃B ∀y (y ∈ B ↔ ∃x (x ∈ A ∧ F(x, y)))
gptkbp:usedIn	gptkb:Zermelo-Fraenkel_set_theory
gptkbp:bfsParent	gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice gptkb:Axiomatic_set_theory gptkb:Axiom_Schema_of_Separation gptkb:ZFC_set_theory gptkb:ZF_(Zermelo–Fraenkel_set_theory_without_Choice) gptkb:ZF_(Zermelo–Fraenkel_set_theory_without_choice) gptkb:Zermelo–Fraenkel_set_theory_with_the_Axiom_of_Choice
gptkbp:bfsLayer	7