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 |
|---|---|
| Peano arithmetic | axioms defining addition recursively ⓘ |
| Peano arithmetic | axioms defining multiplication recursively ⓘ |
| Peano arithmetic | induction schema ⓘ |
| Kripke–Platek set theory | Extensionality ⓘ |
| Kripke–Platek set theory | Pairing ⓘ |
| Kripke–Platek set theory | Union ⓘ |
| Kripke–Platek set theory | Infinity ⓘ |
| Kripke–Platek set theory | Δ0-Separation ⓘ |
| Kripke–Platek set theory | Δ0-Collection ⓘ |
| Kripke–Platek set theory | Foundation ⓘ |
|
John
surface form:
John Playfair
|
Playfair’s axiom via predicate surface "hasAxiomNamedAfter" NERFINISHED ⓘ |
| Kleene algebra | associativity of addition ⓘ |
| Kleene algebra | associativity of multiplication ⓘ |
| Kleene algebra | commutativity of addition ⓘ |
| Kleene algebra | distributivity of multiplication over addition ⓘ |
| Kleene algebra | idempotence of addition ⓘ |
| Kleene algebra | zero as additive identity ⓘ |
| Kleene algebra | one as multiplicative identity ⓘ |
| Kleene algebra | annihilation of zero under multiplication ⓘ |
| Kleene algebra | star unfold law ⓘ |
| Kleene algebra | star induction law ⓘ |
| algebraic quantum field theory | Haag duality in some models ⓘ |
| Stiefel–Whitney classes | Whitney sum formula via predicate surface "axiomatizedBy" NERFINISHED ⓘ |
| Stiefel–Whitney classes | naturality via predicate surface "axiomatizedBy" ⓘ |
| Stiefel–Whitney classes | normalization on trivial bundles via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | commutativity via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | associativity via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | distributivity via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | identity laws via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | complement laws via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | idempotent laws via predicate surface "axiomatizedBy" ⓘ |
| Boolean algebra | absorption laws via predicate surface "axiomatizedBy" ⓘ |
| homotopy type theory | univalence axiom ⓘ |