Feferman–Schütte ordinal

E513379

countable ordinal large countable ordinal ordinal number proof-theoretic ordinal

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.

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Observed surface forms (1)

Surface form	Occurrences
Feferman–Schütte ordinal Γ₀	2

Statements (44)

Predicate	Object
instanceOf	countable ordinal ⓘ large countable ordinal ⓘ ordinal number ⓘ proof-theoretic ordinal ⓘ
alsoKnownAs	Γ₀ NERFINISHED ⓘ
appearsInWorkOf	Kurt Schütte NERFINISHED ⓘ Solomon Feferman NERFINISHED ⓘ
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 NERFINISHED ⓘ
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 NERFINISHED ⓘ
marksBoundaryOf	predicative mathematics ⓘ predicative provability strength ⓘ
namedAfter	Kurt Schütte NERFINISHED ⓘ Solomon Feferman NERFINISHED ⓘ
roleInProofTheory	ordinal of predicative analysis ⓘ proof-theoretic ordinal of predicative arithmetic and analysis ⓘ
symbol	Γ₀ NERFINISHED ⓘ
topicIn	predicativity debates in foundations of mathematics ⓘ proof-theoretic ordinal classification ⓘ
usedIn	foundations of mathematics ⓘ ordinal analysis ⓘ proof theory ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Solomon Feferman → notableIdea → Feferman–Schütte ordinal ⓘ

Veblen hierarchy → relatedTo → Feferman–Schütte ordinal ⓘ

this entity surface form: Feferman–Schütte ordinal Γ₀

Veblen hierarchy → canReach → Feferman–Schütte ordinal ⓘ

this entity surface form: Feferman–Schütte ordinal Γ₀