hasAxiom

P12252
predicate

Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.

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All labels observed (14)

Label Occurrences
hasAxiom canonical 99
axiomatizedBy 13
axiom 9

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 additivity axiom ⓘ
linked to: Shannon entropy
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" ⓘ
von Neumann universe von Neumann universe via predicate surface "pairingAxiomHoldsIn" ⓘ
von Neumann universe von Neumann universe via predicate surface "unionAxiomHoldsIn" ⓘ
von Neumann universe von Neumann universe via predicate surface "powerSetAxiomHoldsIn" ⓘ
von Neumann universe von Neumann universe via predicate surface "infinityAxiomHoldsIn" ⓘ
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 group
linked to: Abelian groups
closure under group operation ⓘ
Abelian group
linked to: Abelian groups
associativity of group operation ⓘ
Abelian group
linked to: Abelian groups
existence of identity element ⓘ
Abelian group
linked to: Abelian groups
existence of inverses ⓘ
Abelian group
linked to: Abelian groups
commutativity of group operation ⓘ
Born rule
linked to: Born rule in quantum mechanics
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 ⓘ