Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:alsoKnownAs |
gptkb:Axiom_of_foundation
|
| gptkbp:category |
gptkb:logic
gptkb:Set_theory |
| gptkbp:compatibleWith |
All set theories
|
| gptkbp:expressedIn |
gptkb:First-order_logic
|
| gptkbp:guarantees |
No set is an element of itself
Every non-empty set A contains an element disjoint from A |
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of regularity
|
| gptkbp:implies |
No infinite descending ∈-chains
No set contains itself as a member |
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:prevention |
Infinite descending membership chains
|
| gptkbp:statedIn |
gptkb:John_von_Neumann
|
| gptkbp:symbol |
∀A [A ≠ ∅ ⇒ ∃B (B ∈ A ∧ A ∩ B = ∅)]
|
| gptkbp:usedIn |
Standard set theory
|
| gptkbp:yearProposed |
1925
|
| gptkbp:bfsParent |
gptkb:Menge
|
| gptkbp:bfsLayer |
5
|