hasAxiom
P12252
predicate
Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
Observed surface forms (8)
- extensionalityAxiomHoldsIn ×1
- includesAxiom ×1
- infinityAxiomHoldsIn ×1
- isPostulateIn ×1
- pairingAxiomHoldsIn ×1
- powerSetAxiomHoldsIn ×1
- unionAxiomHoldsIn ×1
- usesAxiom ×1
Sample triples (63)
| Subject | Object |
|---|---|
|
Abelian groups
surface form:
Abelian group
|
associativity of group operation ⓘ |
|
Abelian groups
surface form:
Abelian group
|
closure under group operation ⓘ |
|
Abelian groups
surface form:
Abelian group
|
commutativity of group operation ⓘ |
|
Abelian groups
surface form:
Abelian group
|
existence of identity element ⓘ |
|
Abelian groups
surface form:
Abelian group
|
existence of inverses ⓘ |
|
Born rule in quantum mechanics
surface form:
Born rule
|
Copenhagen interpretation of quantum mechanics via predicate surface "isPostulateIn" ⓘ |
| Frege’s system in "Grundgesetze der Arithmetik" | Basic Law V via predicate surface "includesAxiom" ⓘ |
| Morse–Kelley set theory by class–set distinction | axioms for sets similar to ZFC ⓘ |
| Morse–Kelley set theory by class–set distinction | class comprehension schema ⓘ |
| Morse–Kelley set theory by class–set distinction | extensionality for classes ⓘ |
| Morse–Kelley set theory by class–set distinction | global choice (in some formulations) ⓘ |
| Shannon–Khinchin axioms |
Shannon entropy
ⓘ
surface form:
Shannon additivity axiom
|
| Shannon–Khinchin axioms | additivity axiom ⓘ |
| Shannon–Khinchin axioms | continuity axiom ⓘ |
| Shannon–Khinchin axioms | continuity in probabilities ⓘ |
| Shannon–Khinchin axioms | expansibility axiom ⓘ |
| Shannon–Khinchin axioms | expansibility with zero-probability events ⓘ |
| Shannon–Khinchin axioms | maximal entropy for the uniform distribution ⓘ |
| Shannon–Khinchin axioms | maximality axiom ⓘ |
| Shannon–Khinchin axioms | recursivity axiom ⓘ |
| Shannon–Khinchin axioms | recursivity for compound experiments ⓘ |
| Shannon–Khinchin axioms | symmetry axiom ⓘ |
| ZF | axiom of empty set ⓘ |
| ZF | axiom of extensionality ⓘ |
| ZF | axiom of foundation ⓘ |
| ZF | axiom of infinity ⓘ |
| ZF | axiom of pairing ⓘ |
| ZF | axiom of power set ⓘ |
| ZF | axiom of union ⓘ |
| ZF | axiom schema of replacement ⓘ |
| ZF | axiom schema of separation ⓘ |
| Zermelo set theory | axiom of choice ⓘ |
| Zermelo set theory | axiom of empty set ⓘ |
| Zermelo set theory | axiom of extensionality ⓘ |
| Zermelo set theory | axiom of infinity ⓘ |
| Zermelo set theory | axiom of pairing ⓘ |
| Zermelo set theory | axiom of power set ⓘ |
| Zermelo set theory | axiom of union ⓘ |
| Zermelo set theory | axiom schema of separation ⓘ |
| Zermelo–Fraenkel set theory | axiom of empty set ⓘ |
| Zermelo–Fraenkel set theory | axiom of extensionality ⓘ |
| Zermelo–Fraenkel set theory | axiom of infinity ⓘ |
| Zermelo–Fraenkel set theory | axiom of pairing ⓘ |
| Zermelo–Fraenkel set theory | axiom of power set ⓘ |
| Zermelo–Fraenkel set theory | axiom of regularity ⓘ |
| Zermelo–Fraenkel set theory | axiom of union ⓘ |
| Zermelo–Fraenkel set theory | axiom schema of replacement ⓘ |
| Zermelo–Fraenkel set theory | axiom schema of separation ⓘ |
| von Neumann paradox in set theory | axiom of choice via predicate surface "usesAxiom" ⓘ |
| von Neumann universe | von Neumann universe via predicate surface "extensionalityAxiomHoldsIn" self-link ⓘ |