Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:alsoKnownAs |
gptkb:Axiom_of_regularity
|
| gptkbp:contrastsWith |
Non-well-founded set theory
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
gptkb:John_von_Neumann |
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of foundation
|
| gptkbp:implies |
Set membership is well-founded
|
| gptkbp:introducedIn |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:language |
gptkb:First-order_logic
|
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:prevention |
Infinite descending membership chains
Sets containing themselves as members |
| gptkbp:state |
Every non-empty set A contains an element that is disjoint from A
|
| gptkbp:symbol |
∀A [A ≠ ∅ → ∃B (B ∈ A ∧ A ∩ B = ∅)]
|
| gptkbp:usedIn |
Standard set theory
|
| gptkbp:bfsParent |
gptkb:Axiom_of_regularity
|
| gptkbp:bfsLayer |
6
|