Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:category |
gptkb:logic
gptkb:Set_theory |
| gptkbp:consequence |
Existence of rank hierarchy
Existence of von Neumann universe |
| gptkbp:enables |
gptkb:Cumulative_hierarchy
Construction of large sets Ordinal arithmetic Transfinite recursion |
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel |
| gptkbp:generalizes |
gptkb:Axiom_of_Separation
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Replacement
|
| gptkbp:introducedIn |
1922
|
| gptkbp:isAxiomOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:relatedTo |
gptkb:Axiom_of_Power_Set
gptkb:Axiom_of_Collection gptkb:Axiom_schema_of_specification |
| 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 ∧ y = F(x)))
|
| gptkbp:usedIn |
gptkb:ZFC
|
| gptkbp:bfsParent |
gptkb:set_theory
|
| gptkbp:bfsLayer |
4
|