Triple

T1509459
Position Surface form Disambiguated ID Type / Status
Subject Pavel Alexandrov E33979 entity
Predicate notableWork P4 FINISHED
Object 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.
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 (with Andrey Kolmogorov) | Statement: [Pavel Alexandrov, notableWork, Foundations of Set Theory (with Andrey Kolmogorov)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Foundations of Set Theory (with Andrey Kolmogorov)
Context triple: [Pavel Alexandrov, notableWork, Foundations of Set Theory (with Andrey Kolmogorov)]
  • A. Remarks on the Foundations of Mathematics
    Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
  • B. 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.
  • C. 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.
  • D. Morse–Kelley set theory by class–set distinction
    Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
  • E. Ulam problem in set theory
    The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
  • 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 (with Andrey Kolmogorov)
Triple: [Pavel Alexandrov, notableWork, Foundations of Set Theory (with Andrey Kolmogorov)]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Foundations of Set Theory (with Andrey Kolmogorov)
Target entity description: "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.
  • A. Remarks on the Foundations of Mathematics
    Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
  • B. 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.
  • C. 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.
  • D. Morse–Kelley set theory by class–set distinction
    Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
  • E. Ulam problem in set theory
    The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
  • 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_69a885f352a4819099b24ff15489dede completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a8891daf708190a23d6c920eac8b6d completed March 4, 2026, 7:33 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad233c254c8190b52b34526c9cb3cb completed March 8, 2026, 7:20 a.m.
NEDg Description generation batch_69ad242d20448190a27ff7414d9cff21 completed March 8, 2026, 7:24 a.m.
NED2 Entity disambiguation (via description) batch_69ad24e6e9688190a20c67c181936e98 completed March 8, 2026, 7:27 a.m.
Created at: March 4, 2026, 7:24 p.m.