Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:category |
gptkb:logic
gptkb:Set_theory |
| gptkbp:guarantees |
For every set, its power set exists as a set.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of power set
|
| gptkbp:implies |
Power set
|
| gptkbp:introduced |
gptkb:Ernst_Zermelo
|
| gptkbp:introducedIn |
1908
|
| gptkbp:partOf |
gptkb:Zermelo-Fraenkel_set_theory
|
| gptkbp:relatedTo |
gptkb:Axiom_of_extensionality
gptkb:Axiom_of_infinity gptkb:Axiom_of_pairing gptkb:Axiom_of_union |
| gptkbp:state |
For any set x, there is a set y such that the elements of y are exactly the subsets of x.
|
| gptkbp:symbol |
∀x ∃y ∀z (z ∈ y ↔ z ⊆ x)
|
| gptkbp:usedIn |
gptkb:ZFC
gptkb:Set_theory |
| gptkbp:bfsParent |
gptkb:Menge
|
| gptkbp:bfsLayer |
5
|