Triple

T20836733
Position Surface form Disambiguated ID Type / Status
Subject Saharon Shelah E512976 entity
Predicate notableIdea P4 FINISHED
Object Shelah’s stability spectrum theorem
Shelah’s stability spectrum theorem is a fundamental result in model theory that classifies first-order theories by describing exactly when they are stable in terms of the number of types over models of different cardinalities.
E1453623 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: Shelah’s stability spectrum theorem | Statement: [Saharon Shelah, notableIdea, Shelah’s stability spectrum theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Shelah’s stability spectrum theorem
Context triple: [Saharon Shelah, notableIdea, Shelah’s stability spectrum theorem]
  • A. Shelah’s eventual categoricity conjecture
    Shelah’s eventual categoricity conjecture is a central open problem in model theory that predicts when a complete first-order theory is determined up to isomorphism by having a unique model in sufficiently large cardinalities.
  • B. Classification Theory for Abstract Elementary Classes
    "Classification Theory for Abstract Elementary Classes" is a foundational work by Saharon Shelah that extends model-theoretic classification theory to the broader framework of abstract elementary classes, analyzing their structural and stability properties.
  • C. Shelah’s singular cardinal theory
    Shelah’s singular cardinal theory is a major area of set theory developed by Saharon Shelah that investigates the behavior and arithmetic of singular cardinals, leading to deep results about cardinal exponentiation and the structure of the set-theoretic universe.
  • D. Vaught conjecture
    The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
  • E. Skolem hulls
    Skolem hulls are the smallest substructures of a model that contain a given set of elements and are closed under all definable Skolem functions, playing a key role in constructing countable elementary submodels in model theory.
  • 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: Shelah’s stability spectrum theorem
Triple: [Saharon Shelah, notableIdea, Shelah’s stability spectrum theorem]
Generated description
Shelah’s stability spectrum theorem is a fundamental result in model theory that classifies first-order theories by describing exactly when they are stable in terms of the number of types over models of different cardinalities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Shelah’s stability spectrum theorem
Target entity description: Shelah’s stability spectrum theorem is a fundamental result in model theory that classifies first-order theories by describing exactly when they are stable in terms of the number of types over models of different cardinalities.
  • A. Shelah’s eventual categoricity conjecture
    Shelah’s eventual categoricity conjecture is a central open problem in model theory that predicts when a complete first-order theory is determined up to isomorphism by having a unique model in sufficiently large cardinalities.
  • B. Classification Theory for Abstract Elementary Classes
    "Classification Theory for Abstract Elementary Classes" is a foundational work by Saharon Shelah that extends model-theoretic classification theory to the broader framework of abstract elementary classes, analyzing their structural and stability properties.
  • C. Shelah’s singular cardinal theory
    Shelah’s singular cardinal theory is a major area of set theory developed by Saharon Shelah that investigates the behavior and arithmetic of singular cardinals, leading to deep results about cardinal exponentiation and the structure of the set-theoretic universe.
  • D. Vaught conjecture
    The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
  • E. Skolem hulls
    Skolem hulls are the smallest substructures of a model that contain a given set of elements and are closed under all definable Skolem functions, playing a key role in constructing countable elementary submodels in model theory.
  • 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_69e0b4cf62a88190bbf92351e9e57259 completed April 16, 2026, 10:07 a.m.
NER Named-entity recognition batch_69e6c326daec8190bd4caa41a4b38833 completed April 21, 2026, 12:21 a.m.
NED1 Entity disambiguation (via context triple) batch_6a090afd181c81909dba7617c286af58 completed May 17, 2026, 12:25 a.m.
NEDg Description generation batch_6a090c524a308190bb063e0f5200cef7 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, 12:42 p.m.