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 |
|---|---|
| Zermelo set theory | axiom of power set ⓘ |
| Zermelo set theory | axiom of infinity ⓘ |
| Zermelo set theory | axiom schema of separation ⓘ |
| Zermelo set theory | axiom of choice ⓘ |
| ZF | axiom of extensionality ⓘ |
| ZF | axiom of empty set ⓘ |
| ZF | axiom of pairing ⓘ |
| ZF | axiom of union ⓘ |
| ZF | axiom of power set ⓘ |
| ZF | axiom schema of separation ⓘ |
| ZF | axiom schema of replacement ⓘ |
| ZF | axiom of infinity ⓘ |
| ZF | axiom of foundation ⓘ |
| Arrow’s impossibility theorem | unrestricted domain via predicate surface "axiom" ⓘ |
| Arrow’s impossibility theorem | Pareto efficiency via predicate surface "axiom" ⓘ |
| Arrow’s impossibility theorem | independence of irrelevant alternatives via predicate surface "axiom" ⓘ |
| Arrow’s impossibility theorem | non-dictatorship via predicate surface "axiom" ⓘ |
| Arrow’s impossibility theorem | transitivity of the social preference relation via predicate surface "axiom" ⓘ |
| Arrow’s impossibility theorem | completeness of the social preference relation via predicate surface "axiom" ⓘ |
| Blum complexity measures | domain condition ⓘ |
| Blum complexity measures | decidability condition ⓘ |
| Blum complexity measures | Blum axioms ⓘ |
| Blum complexity measures | complexity is defined exactly on halting computations via predicate surface "axiom1" ⓘ |
| topological quantum field theory | Michael Atiyah via predicate surface "axiomatizedBy" ⓘ |
| Borda count | Young’s characterization using neutrality, anonymity, reinforcement, and continuity via predicate surface "axiomatizedBy" ⓘ |
| Borda count | various scoring-rule axiomatizations in social choice theory via predicate surface "axiomatizedBy" ⓘ |
|
Probability Theory
surface form:
Probability theory
|
Kolmogorov axioms via predicate surface "axiomatizedIn" ⓘ |
| Weil cohomology | functoriality ⓘ |
| Weil cohomology | finite-dimensionality ⓘ |
| Weil cohomology | Poincaré duality ⓘ |
| Weil cohomology | Künneth formula ⓘ |
| Weil cohomology | cycle class map ⓘ |
| Weil cohomology |
Hard Lefschetz theorem
ⓘ
surface form:
hard Lefschetz theorem
|
| Weil cohomology |
Lefschetz fixed-point theorem
ⓘ
surface form:
Lefschetz trace formula
|
| Weil cohomology | homotopy invariance ⓘ |
| Weil cohomology | excision ⓘ |
| Weil cohomology |
Mayer–Vietoris sequence in de Rham cohomology
ⓘ
surface form:
Mayer–Vietoris sequence
|
| Selberg class | Dirichlet series representation ⓘ |
| Selberg class | analytic continuation ⓘ |
| Selberg class | functional equation ⓘ |
| Selberg class |
Euler product formula for the Riemann zeta function
ⓘ
surface form:
Euler product
|
| Selberg class | Ramanujan hypothesis type growth condition ⓘ |
| Dmitry Faddeev | Faddeev’s axioms via predicate surface "hasAxiomNamedAfter" ⓘ |
| Kolmogorov axioms | non-negativity of probability via predicate surface "axiom" ⓘ |
| Kolmogorov axioms | normalization of probability via predicate surface "axiom" ⓘ |
| Kolmogorov axioms | countable additivity of probability via predicate surface "axiom" ⓘ |
| Peano arithmetic | 0 is a natural number ⓘ |
| Peano arithmetic | every natural number has a unique successor ⓘ |
| Peano arithmetic | 0 is not the successor of any natural number ⓘ |
| Peano arithmetic | distinct natural numbers have distinct successors ⓘ |