Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:category |
gptkb:logic
gptkb:Foundations_of_mathematics |
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
1908 |
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Empty Set
|
| gptkbp:implies |
Existence of the empty set
|
| gptkbp:partOf |
gptkb:Zermelo-Fraenkel_set_theory
|
| gptkbp:relatedTo |
gptkb:Axiom_of_Extensionality
gptkb:Axiom_of_Infinity |
| gptkbp:state |
There exists a set with no elements
|
| gptkbp:symbol |
∃x ∀y (¬(y ∈ x))
|
| gptkbp:usedIn |
gptkb:ZF
gptkb:ZFC gptkb:Set_theory |
| gptkbp:bfsParent |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Axiom_of_Pairing gptkb:Zermelo-Fraenkel_set_theory |
| gptkbp:bfsLayer |
5
|