hasAxiom
P12252
predicate
Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
All labels observed (14)
| Label | Occurrences |
|---|---|
| hasAxiom canonical | 99 |
| axiomatizedBy | 13 |
| axiom | 9 |
| hasAxiomNamedAfter | 2 |
| axiom1 | 1 |
| axiomatizedIn | 1 |
| extensionalityAxiomHoldsIn | 1 |
| includesAxiom | 1 |
| infinityAxiomHoldsIn | 1 |
| isPostulateIn | 1 |
| pairingAxiomHoldsIn | 1 |
| powerSetAxiomHoldsIn | 1 |
| unionAxiomHoldsIn | 1 |
| usesAxiom | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasAxiom
Generated description
Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
Sample triples (133)
| Subject | Object |
|---|---|
| Shannon–Khinchin axioms | continuity axiom ⓘ |
| Shannon–Khinchin axioms | maximality axiom ⓘ |
| Shannon–Khinchin axioms | expansibility axiom ⓘ |
| Shannon–Khinchin axioms | recursivity axiom ⓘ |
| Shannon–Khinchin axioms | additivity axiom ⓘ |
| Shannon–Khinchin axioms |
Shannon entropy
ⓘ
surface form:
Shannon additivity axiom
|
| Shannon–Khinchin axioms | symmetry axiom ⓘ |
| Shannon–Khinchin axioms | continuity in probabilities ⓘ |
| Shannon–Khinchin axioms | maximal entropy for the uniform distribution ⓘ |
| Shannon–Khinchin axioms | expansibility with zero-probability events ⓘ |
| Shannon–Khinchin axioms | recursivity for compound experiments ⓘ |
| Zermelo–Fraenkel set theory | axiom of extensionality ⓘ |
| Zermelo–Fraenkel set theory | axiom of empty set ⓘ |
| Zermelo–Fraenkel set theory | axiom of pairing ⓘ |
| Zermelo–Fraenkel set theory | axiom of union ⓘ |
| Zermelo–Fraenkel set theory | axiom of power set ⓘ |
| Zermelo–Fraenkel set theory | axiom of infinity ⓘ |
| Zermelo–Fraenkel set theory | axiom schema of separation ⓘ |
| Zermelo–Fraenkel set theory | axiom schema of replacement ⓘ |
| Zermelo–Fraenkel set theory | axiom of regularity ⓘ |
| von Neumann universe | von Neumann universe via predicate surface "extensionalityAxiomHoldsIn" self-link ⓘ |
| von Neumann universe | von Neumann universe via predicate surface "pairingAxiomHoldsIn" self-link ⓘ |
| von Neumann universe | von Neumann universe via predicate surface "unionAxiomHoldsIn" self-link ⓘ |
| von Neumann universe | von Neumann universe via predicate surface "powerSetAxiomHoldsIn" self-link ⓘ |
| von Neumann universe | von Neumann universe via predicate surface "infinityAxiomHoldsIn" self-link ⓘ |
| von Neumann paradox in set theory | axiom of choice via predicate surface "usesAxiom" ⓘ |
| Frege’s system in "Grundgesetze der Arithmetik" | Basic Law V via predicate surface "includesAxiom" ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of extensionality ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of empty set ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of pairing ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of union ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of infinity ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of replacement (for sets) ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom schema of class comprehension (restricted) ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of foundation ⓘ |
| von Neumann–Bernays–Gödel set theory | axiom of choice (for sets) ⓘ |
|
Abelian groups
surface form:
Abelian group
|
closure under group operation ⓘ |
|
Abelian groups
surface form:
Abelian group
|
associativity of group operation ⓘ |
|
Abelian groups
surface form:
Abelian group
|
existence of identity element ⓘ |
|
Abelian groups
surface form:
Abelian group
|
existence of inverses ⓘ |
|
Abelian groups
surface form:
Abelian group
|
commutativity of group operation ⓘ |
|
Born rule in quantum mechanics
surface form:
Born rule
|
Copenhagen interpretation of quantum mechanics via predicate surface "isPostulateIn" ⓘ |
| 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) ⓘ |
| Zermelo set theory | axiom of extensionality ⓘ |
| Zermelo set theory | axiom of empty set ⓘ |
| Zermelo set theory | axiom of pairing ⓘ |
| Zermelo set theory | axiom of union ⓘ |