Statements (20)
| 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:John_von_Neumann
1922 |
| 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: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 ∧ B ∩ A = ∅)]
|
| gptkbp:usedIn |
Standard set theory
|
| gptkbp:bfsParent |
gptkb:Morse–Kelley_set_theory
gptkb:Axiom_of_Infinity gptkb:Axiom_of_Regularity gptkb:Set_Theory |
| gptkbp:bfsLayer |
5
|