Turing degrees
E679185
equivalence classes under Turing reducibility
mathematical concept
structure in computability theory
Turing degrees are an abstract classification of sets of natural numbers or decision problems according to their relative level of algorithmic unsolvability or computational complexity under Turing reducibility.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Turing degrees canonical | 3 |
| Turing degree | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7666827 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Turing degrees Context triple: [Computability Theory, fieldOfStudy, Turing degrees]
-
A.
Computability Theory
Computability Theory is a branch of theoretical computer science and mathematical logic that studies which problems can be solved by algorithms and how efficiently they can be computed.
-
B.
Kleene hierarchy
The Kleene hierarchy is a classification of sets and predicates in arithmetic and recursion theory based on their definability and complexity, introduced by logician Stephen Kleene.
-
C.
Kolmogorov complexity
Kolmogorov complexity is a measure of the amount of information in an object, defined as the length of the shortest computer program that can produce it.
-
D.
Rice's theorem
Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
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E.
Blum–Shub–Smale model of computation
The Blum–Shub–Smale model of computation is a theoretical framework for analyzing algorithms over real numbers, extending classical complexity theory beyond discrete computation.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Turing degrees Target entity description: Turing degrees are an abstract classification of sets of natural numbers or decision problems according to their relative level of algorithmic unsolvability or computational complexity under Turing reducibility.
-
A.
Computability Theory
Computability Theory is a branch of theoretical computer science and mathematical logic that studies which problems can be solved by algorithms and how efficiently they can be computed.
-
B.
Kleene hierarchy
The Kleene hierarchy is a classification of sets and predicates in arithmetic and recursion theory based on their definability and complexity, introduced by logician Stephen Kleene.
-
C.
Kolmogorov complexity
Kolmogorov complexity is a measure of the amount of information in an object, defined as the length of the shortest computer program that can produce it.
-
D.
Rice's theorem
Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
-
E.
Blum–Shub–Smale model of computation
The Blum–Shub–Smale model of computation is a theoretical framework for analyzing algorithms over real numbers, extending classical complexity theory beyond discrete computation.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
equivalence classes under Turing reducibility
ⓘ
mathematical concept ⓘ structure in computability theory ⓘ |
| basedOn | Turing reducibility ⓘ |
| captures |
relative algorithmic unsolvability
ⓘ
relative computational complexity ⓘ |
| connectedTo |
effective descriptive set theory
ⓘ
set of reals under Turing reducibility ⓘ |
| definedOn |
decision problems
ⓘ
sets of natural numbers ⓘ |
| equivalenceClassOf | sets of natural numbers mutually Turing reducible to each other ⓘ |
| equivalenceRelation | mutual Turing reducibility ⓘ |
| field |
computability theory
ⓘ
mathematical logic ⓘ recursion theory ⓘ |
| formalizedIn | second-order arithmetic ⓘ |
| hasBottomElement | degree of computable sets ⓘ |
| hasOpenProblems |
automorphism group of the Turing degrees
ⓘ
exact lattice-theoretic properties of the degrees ⓘ |
| hasOperation | join ⓘ |
| hasProperty |
contains high and low degrees
ⓘ
contains incomparable degrees ⓘ contains minimal degrees ⓘ every nonzero degree bounds a minimal degree ⓘ not a lattice under Turing reducibility ⓘ uncountable set of degrees ⓘ |
| hasStructure | upper semilattice ⓘ |
| hasTopElement | degree of the halting problem ⓘ |
| introducedInField | mid 20th century computability theory ⓘ |
| namedAfter | Alan Turing ⓘ |
| orderType | partial order under Turing reducibility ⓘ |
| relatedTo |
Medvedev degrees
ⓘ
Muchnik degrees ⓘ Turing jump ⓘ arithmetical hierarchy ⓘ
linked to:
Kleene hierarchy
degrees of unsolvability ⓘ hyperarithmetical hierarchy ⓘ many-one degrees ⓘ truth-table degrees ⓘ |
| studiedBy |
Alan Turing
ⓘ
Emil Post ⓘ Lachlan ⓘ Sacks ⓘ Shore ⓘ Slaman ⓘ Stephen Kleene ⓘ |
| symbol | D_T ⓘ |
| usedFor |
analyzing the structure of unsolvable problems
ⓘ
classifying decision problems by relative computability ⓘ studying relative computability of real numbers ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Turing degrees Description of subject: Turing degrees are an abstract classification of sets of natural numbers or decision problems according to their relative level of algorithmic unsolvability or computational complexity under Turing reducibility.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Turing degrees