Triple

T16445528
Position Surface form Disambiguated ID Type / Status
Subject Abraham Fraenkel E399413 entity
Predicate notableWork P4 FINISHED
Object Foundations of Set Theory
Foundations of Set Theory is a seminal mathematical text by Abraham Fraenkel that systematically develops modern axiomatic set theory and its foundations.
E173183 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: Foundations of Set Theory | Statement: [Abraham Fraenkel, notableWork, Foundations of Set Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Foundations of Set Theory
Context triple: [Abraham Fraenkel, notableWork, Foundations of Set Theory]
  • A. Set Theory and Its Logic
    Set Theory and Its Logic is a foundational work by W.V.O. Quine that develops set theory within a rigorous logical framework, exploring its axioms, paradoxes, and philosophical implications.
  • 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. Introduction to Set Theory
    Introduction to Set Theory is a foundational mathematics textbook that presents the basic concepts, methods, and results of modern set theory for advanced undergraduates and beginning graduate students.
  • D. 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.
  • E. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern 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: Foundations of Set Theory
Triple: [Abraham Fraenkel, notableWork, Foundations of Set Theory]
Generated description
Foundations of Set Theory is a seminal mathematical text by Abraham Fraenkel that systematically develops modern axiomatic set theory and its foundations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Foundations of Set Theory
Target entity description: Foundations of Set Theory is a seminal mathematical text by Abraham Fraenkel that systematically develops modern axiomatic set theory and its foundations.
  • A. Set Theory and Its Logic
    Set Theory and Its Logic is a foundational work by W.V.O. Quine that develops set theory within a rigorous logical framework, exploring its axioms, paradoxes, and philosophical implications.
  • B. Foundations of Set Theory (with Andrey Kolmogorov) chosen
    "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. Introduction to Set Theory
    Introduction to Set Theory is a foundational mathematics textbook that presents the basic concepts, methods, and results of modern set theory for advanced undergraduates and beginning graduate students.
  • D. 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.
  • E. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
  • F. None of above.

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_69d87f2c6778819080fcfae53be8f12a completed April 10, 2026, 4:40 a.m.
NER Named-entity recognition batch_69e32cdb5d908190bb6c5cb3c794cf4b completed April 18, 2026, 7:03 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0045922d748190bb3200c96f244149 completed May 10, 2026, 8:45 a.m.
NEDg Description generation batch_6a00473d31308190ab836c09da2a82da completed May 10, 2026, 8:52 a.m.
NED2 Entity disambiguation (via description) batch_6a0047b4b6688190afef52b39788ceae completed May 10, 2026, 8:54 a.m.
Created at: April 10, 2026, 5:10 a.m.