small Veblen ordinal
E1453668
UNEXPLORED
The small Veblen ordinal is a large countable ordinal that extends the hierarchy of ordinals generated by the Veblen functions far beyond the Feferman–Schütte ordinal and serves as an important benchmark in proof theory and ordinal analysis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| small Veblen ordinal canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T20851739 — 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: small Veblen ordinal Context triple: [Feferman–Schütte ordinal, lessThan, small Veblen ordinal]
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A.
Bachmann–Howard ordinal
The Bachmann–Howard ordinal is a large countable ordinal that serves as a key benchmark in proof theory, marking the strength of powerful formal systems extending predicative arithmetic.
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B.
Feferman–Schütte 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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C.
Cantor normal form
Cantor normal form is a canonical way of expressing any ordinal number as a finite sum of decreasing powers of the first infinite ordinal ω with natural number coefficients.
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D.
Woodin cardinal
A Woodin cardinal is a large cardinal in set theory with strong consistency and determinacy properties, central to modern research on the foundations of mathematics and descriptive set theory.
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E.
Aleph (mathematics)
Aleph (mathematics) denotes the infinite cardinal numbers used in set theory to measure and compare the sizes of infinite sets.
- 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: small Veblen ordinal Target entity description: The small Veblen ordinal is a large countable ordinal that extends the hierarchy of ordinals generated by the Veblen functions far beyond the Feferman–Schütte ordinal and serves as an important benchmark in proof theory and ordinal analysis.
-
A.
Bachmann–Howard ordinal
The Bachmann–Howard ordinal is a large countable ordinal that serves as a key benchmark in proof theory, marking the strength of powerful formal systems extending predicative arithmetic.
-
B.
Feferman–Schütte 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.
-
C.
Cantor normal form
Cantor normal form is a canonical way of expressing any ordinal number as a finite sum of decreasing powers of the first infinite ordinal ω with natural number coefficients.
-
D.
Woodin cardinal
A Woodin cardinal is a large cardinal in set theory with strong consistency and determinacy properties, central to modern research on the foundations of mathematics and descriptive set theory.
-
E.
Aleph (mathematics)
Aleph (mathematics) denotes the infinite cardinal numbers used in set theory to measure and compare the sizes of infinite sets.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.