Triple

T11736264
Position Surface form Disambiguated ID Type / Status
Subject Barkley Rosser E279033 entity
Predicate notableWork P4 FINISHED
Object Rosser trick
The Rosser trick is a refinement of Gödel’s incompleteness proof that avoids using ω-consistency by constructing a self-referential sentence asserting that a shorter proof of its negation exists.
E943471 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: Rosser trick | Statement: [Barkley Rosser, notableWork, Rosser trick]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Rosser trick
Context triple: [Barkley Rosser, notableWork, Rosser trick]
  • A. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • B. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • C. Tarski's undefinability theorem
    Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
  • D. Kleene’s recursion theorem
    Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
  • E. Gentzen’s consistency proof for arithmetic
    Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
  • 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: Rosser trick
Triple: [Barkley Rosser, notableWork, Rosser trick]
Generated description
The Rosser trick is a refinement of Gödel’s incompleteness proof that avoids using ω-consistency by constructing a self-referential sentence asserting that a shorter proof of its negation exists.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Rosser trick
Target entity description: The Rosser trick is a refinement of Gödel’s incompleteness proof that avoids using ω-consistency by constructing a self-referential sentence asserting that a shorter proof of its negation exists.
  • A. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • B. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • C. Tarski's undefinability theorem
    Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
  • D. Kleene’s recursion theorem
    Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
  • E. Gentzen’s consistency proof for arithmetic
    Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
  • 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_69d6aaffec6881908bead509e8621742 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8a4edced48190b7a59dd45921828e completed April 10, 2026, 7:21 a.m.
NED1 Entity disambiguation (via context triple) batch_69f019b318188190bfb7effcf42974d2 completed April 28, 2026, 2:21 a.m.
NEDg Description generation batch_69f0319271788190a105828ae7582668 completed April 28, 2026, 4:03 a.m.
NED2 Entity disambiguation (via description) batch_69f05a44dcb88190a0bb57b0c8fef6b9 completed April 28, 2026, 6:57 a.m.
Created at: April 8, 2026, 9:41 p.m.