Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:alsoKnownAs |
gptkb:Axiom_of_Foundation
|
| gptkbp:category |
gptkb:Mathematics
gptkb:logic |
| gptkbp:compatibleWith |
Non-well-founded set theory
|
| gptkbp:formedBy |
1920s
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Regularity
|
| gptkbp:implies |
No set is an element of itself
The membership relation is well-founded |
| gptkbp:partOf |
gptkb:Zermelo-Fraenkel_set_theory
|
| gptkbp:prevention |
Infinite descending membership chains
Sets being members of themselves |
| gptkbp:state |
Every non-empty set A contains an element that is disjoint from A
|
| gptkbp:statedIn |
gptkb:John_von_Neumann
|
| gptkbp:symbol |
∀A [A ≠ ∅ → ∃B (B ∈ A ∧ A ∩ B = ∅)]
|
| gptkbp:usedIn |
Standard set theory
|
| gptkbp:bfsParent |
gptkb:set_theory
|
| gptkbp:bfsLayer |
4
|