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.