Triple

T3931000
Position Surface form Disambiguated ID Type / Status
Subject Abraham Fraenkel E90792 entity
Predicate notableWork P4 FINISHED
Object Einleitung in die Mengenlehre
Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
E399415 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: Einleitung in die Mengenlehre | Statement: [Abraham Fraenkel, notableWork, Einleitung in die Mengenlehre]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Einleitung in die Mengenlehre
Context triple: [Abraham Fraenkel, notableWork, Einleitung in die Mengenlehre]
  • A. Untersuchungen über die Grundlagen der Mengenlehre
    Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
  • B. Foundations of Set Theory (with Andrey Kolmogorov)
    "Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set theory.
  • C. Zermelo set theory
    Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
  • D. Grundgesetze der Arithmetik, Volume II
    Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
  • E. Zermelo–Fraenkel set theory
    Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
  • 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: Einleitung in die Mengenlehre
Triple: [Abraham Fraenkel, notableWork, Einleitung in die Mengenlehre]
Generated description
Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Einleitung in die Mengenlehre
Target entity description: Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
  • A. Untersuchungen über die Grundlagen der Mengenlehre
    Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
  • B. Foundations of Set Theory (with Andrey Kolmogorov)
    "Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set theory.
  • C. Zermelo set theory
    Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
  • D. Grundgesetze der Arithmetik, Volume II
    Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
  • E. Zermelo–Fraenkel set theory
    Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
  • 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_69aed95f26e0819094b0e71974543a19 completed March 9, 2026, 2:29 p.m.
NER Named-entity recognition batch_69aeeda98058819094dd6ab223670860 completed March 9, 2026, 3:56 p.m.
NED1 Entity disambiguation (via context triple) batch_69b5288408f0819090217513e7a21091 completed March 14, 2026, 9:21 a.m.
NEDg Description generation batch_69b5294a9b80819083124bc2ff6828aa completed March 14, 2026, 9:24 a.m.
NED2 Entity disambiguation (via description) batch_69b529f6a3488190a7a9ae37f71cff56 completed March 14, 2026, 9:27 a.m.
Created at: March 9, 2026, 3:23 p.m.