hasTheorem

P38252

predicate

Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.

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All labels observed (10)

Label	Occurrences
hasTheorem canonical	27
secondTheoremStates	2
EulerTheoremStatement	1
Kirby theorem	1
Matiyasevich’s theorem	1
YauTheorem	1
associatedWithTheorem	1
hasStructureTheorem	1
hasTheoremAsTopic	1
resultByGödel	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: hasTheorem

Generated description

Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.

Sample triples (37)

Subject	Object
Riemann surface linked to: Riemann surfaces	uniformization theorem ⓘ
Riemann surface linked to: Riemann surfaces	Riemann–Roch theorem ⓘ
Riemann surface linked to: Riemann surfaces	Riemann–Hurwitz formula ⓘ
Riemann surface linked to: Riemann surfaces	Hodge decomposition for compact Riemann surfaces ⓘ
Euler’s totient function φ(n)	If gcd(a,n) = 1 then a^{φ(n)} ≡ 1 (mod n) via predicate surface "EulerTheoremStatement" ⓘ
Abelian group linked to: Abelian groups	finitely generated Abelian groups decompose into direct sum of cyclic groups via predicate surface "hasStructureTheorem" ⓘ
Gödel's incompleteness theorems	no consistent, effectively axiomatized theory capable of expressing elementary arithmetic can prove its own consistency via predicate surface "secondTheoremStates" ⓘ
Calabi–Yau manifold	existence of Ricci-flat Kähler metric given c1=0 via predicate surface "YauTheorem" ⓘ
Noetherian ring linked to: Noetherian rings	Hilbert basis theorem: if R is Noetherian then R[x] is Noetherian ⓘ linked to: Hilbert basis theorem
Noetherian ring linked to: Noetherian rings	Lasker–Noether theorem on primary decomposition ⓘ
Noetherian ring linked to: Noetherian rings	Krull’s principal ideal theorem applies to Noetherian rings ⓘ
density functional theory	Hohenberg–Kohn theorem ⓘ
density functional theory	Kohn–Sham equations ⓘ
The Poincaré-Birkhoff-Witt theorem in ring theory	Poincaré–Birkhoff–Witt theorem via predicate surface "hasTheoremAsTopic" ⓘ linked to: The Poincaré-Birkhoff-Witt theorem in ring theory
Bernstein polynomials	Weierstrass approximation theorem via predicate surface "associatedWithTheorem" NERFINISHED ⓘ
Hilbert's first problem	continuum hypothesis is consistent with ZF if ZF is consistent via predicate surface "resultByGödel" ⓘ
geometry of numbers	Minkowski convex body theorem NERFINISHED ⓘ
geometry of numbers	Minkowski linear forms theorem NERFINISHED ⓘ
geometry of numbers	Minkowski lattice point theorem NERFINISHED ⓘ
geometry of numbers	Blichfeldt theorem NERFINISHED ⓘ
geometry of numbers	Hermite constant bounds NERFINISHED ⓘ
geometry of numbers	Mahler compactness theorem NERFINISHED ⓘ
geometry of numbers	Siegel mean value theorem NERFINISHED ⓘ
Hohenberg–Kohn theorem	the correct ground-state density minimizes the energy functional via predicate surface "secondTheoremStates" ⓘ
local class field theory	local reciprocity law ⓘ
local class field theory	existence theorem of local class field theory ⓘ
local class field theory	Hasse–Arf theorem (in the abelian case) NERFINISHED ⓘ
Yuri Matiyasevich	states that every recursively enumerable set of natural numbers is Diophantine via predicate surface "Matiyasevich’s theorem" ⓘ
Kähler geometry	Hodge decomposition theorem for Kähler manifolds NERFINISHED ⓘ
Kähler geometry	Lefschetz decomposition NERFINISHED ⓘ
Kähler geometry	Hard Lefschetz theorem NERFINISHED ⓘ
Kähler geometry	Kähler identities NERFINISHED ⓘ
Kähler geometry	∂∂̄-lemma on Kähler manifolds ⓘ
Kähler geometry	Kodaira embedding theorem NERFINISHED ⓘ
Kähler geometry	Yau's solution of the Calabi conjecture NERFINISHED ⓘ
Kirby calculus	Kirby theorem NERFINISHED ⓘ
Kirby calculus	equivalence of 3-manifolds via surgery corresponds to Kirby moves on framed links via predicate surface "Kirby theorem" ⓘ