Feferman–Schütte ordinal
E513379
The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Feferman–Schütte ordinal Γ₀ | 3 |
| Feferman–Schütte ordinal canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5354241 — 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: Feferman–Schütte ordinal Context triple: [Solomon Feferman, notableIdea, Feferman–Schütte ordinal]
-
A.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
B.
Kripke–Platek set theory
Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
-
C.
Conway chained arrow notation
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
-
D.
Fraenkel
Fraenkel is a surname most prominently associated with Abraham Fraenkel, a German-Israeli mathematician known for his foundational work in axiomatic set theory.
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E.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
- 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: Feferman–Schütte ordinal Target entity description: The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
-
A.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
B.
Kripke–Platek set theory
Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
-
C.
Conway chained arrow notation
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
-
D.
Fraenkel
Fraenkel is a surname most prominently associated with Abraham Fraenkel, a German-Israeli mathematician known for his foundational work in axiomatic set theory.
-
E.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
countable ordinal
ⓘ
large countable ordinal ⓘ ordinal number ⓘ proof-theoretic ordinal ⓘ |
| alsoKnownAs | Γ₀ ⓘ |
| appearsInWorkOf |
Kurt Schütte
ⓘ
Solomon Feferman ⓘ |
| associatedWithSystem |
predicative analysis
ⓘ
predicative second-order arithmetic ⓘ |
| belongsTo | ordinal notation systems for predicative theories ⓘ |
| characterizedAs |
the limit of the sequence φ_0(0), φ_1(0), φ_2(0), … in the Veblen hierarchy
ⓘ
the smallest ordinal α such that φ_α(0)=α in the Veblen hierarchy ⓘ |
| definedUsing | Veblen hierarchy ⓘ |
| field |
mathematical logic
ⓘ
proof theory ⓘ set theory ⓘ |
| greaterThan |
all ordinals reachable by finite iteration of the Veblen function starting from 0
ⓘ
ε₀ ⓘ |
| hasCofinality | ω ⓘ |
| hasProperty |
closed under ordinal addition, multiplication, and exponentiation below it
ⓘ
first impredicative ordinal in many traditional analyses of predicativity ⓘ |
| isAdditivelyIndecomposable | true ⓘ |
| isCountable | true ⓘ |
| isEpsilonNumber | false ⓘ |
| isFirstFixedPointOf | Veblen function φ_α(0) ⓘ |
| isLimitOfIncreasingSequenceOfOrdinals | true ⓘ |
| isLimitOrdinal | true ⓘ |
| isMultiplicativelyIndecomposable | true ⓘ |
| isRecursiveOrdinal | true ⓘ |
| isStrictlyLessThan | Bachmann–Howard ordinal ⓘ |
| isWellOrdered | true ⓘ |
| lessThan | small Veblen ordinal ⓘ |
| marksBoundaryOf |
predicative mathematics
ⓘ
predicative provability strength ⓘ |
| namedAfter |
Kurt Schütte
ⓘ
Solomon Feferman ⓘ |
| roleInProofTheory |
ordinal of predicative analysis
ⓘ
proof-theoretic ordinal of predicative arithmetic and analysis ⓘ |
| symbol | Γ₀ ⓘ |
| topicIn |
predicativity debates in foundations of mathematics
ⓘ
proof-theoretic ordinal classification ⓘ |
| usedIn |
foundations of mathematics
ⓘ
ordinal analysis ⓘ proof theory ⓘ |
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: Feferman–Schütte ordinal Description of subject: The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Feferman–Schütte ordinal
linked to: Feferman–Schütte ordinal
linked to: Feferman–Schütte ordinal