Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
axiom schema
|
| gptkbp:category |
gptkb:axiom_of_ZFC
|
| gptkbp:enables |
ordinal arithmetic
transfinite recursion construction of von Neumann universe |
| gptkbp:expressedIn |
∀A ∀F (function F) ⇒ ∃B ∀y (y ∈ B ⇔ ∃x ∈ A (F(x) = y))
|
| 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:introducedIn |
1922
|
| gptkbp:purpose |
Allows the construction of new sets by replacing elements of a set with other elements according to a definable function
|
| gptkbp:relatedTo |
gptkb:axiom_schema_of_separation
axiom of choice |
| gptkbp:usedIn |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:ZFC |
| gptkbp:bfsParent |
gptkb:Zermelo–Fraenkel_axioms
gptkb:ZFC |
| gptkbp:bfsLayer |
6
|