Triple

T20851739
Position Surface form Disambiguated ID Type / Status
Subject Feferman–Schütte ordinal E513379 entity
Predicate lessThan P11452 FINISHED
Object small Veblen ordinal
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.
E1453668 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: small Veblen ordinal | Statement: [Feferman–Schütte ordinal, lessThan, small Veblen ordinal]
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]
  • 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
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: small Veblen ordinal
Triple: [Feferman–Schütte ordinal, lessThan, small Veblen ordinal]
Generated 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.
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

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e0b4f4898081908209e58edb8f9c45 completed April 16, 2026, 10:07 a.m.
NER Named-entity recognition batch_69e6c3a3d8808190b8efce77ae36850e completed April 21, 2026, 12:24 a.m.
NED1 Entity disambiguation (via context triple) batch_6a090b0790348190b6e89fb12eaff9d8 completed May 17, 2026, 12:25 a.m.
NEDg Description generation batch_6a090c627830819089b0a479efc42536 completed May 17, 2026, 12:31 a.m.
NED2 Entity disambiguation (via description) batch_6a090cd6f0048190861b7a93560355aa completed May 17, 2026, 12:33 a.m.
Created at: April 16, 2026, 12:43 p.m.