Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:alsoKnownAs |
power set axiom
|
| gptkbp:category |
gptkb:logic
gptkb:set_theory |
| gptkbp:guarantees |
for every set, the set of all its subsets exists
|
| 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: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 ⊆ x → z ∈ y)
|
| gptkbp:usedIn |
gptkb:ZFC
gptkb:Zermelo_set_theory |
| gptkbp:bfsParent |
gptkb:Zermelo–Fraenkel_axioms
gptkb:Axiom_schema_of_separation |
| gptkbp:bfsLayer |
6
|