Triple

T3930985
Position Surface form Disambiguated ID Type / Status
Subject Abraham Fraenkel E90792 entity
Predicate knownFor P22 FINISHED
Object Fraenkel–Mostowski permutation models
Fraenkel–Mostowski permutation models are set-theoretic constructions using permutations of atoms to demonstrate the independence of certain choice principles from Zermelo–Fraenkel set theory.
E399414 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: Fraenkel–Mostowski permutation models | Statement: [Abraham Fraenkel, knownFor, Fraenkel–Mostowski permutation models]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fraenkel–Mostowski permutation models
Context triple: [Abraham Fraenkel, knownFor, Fraenkel–Mostowski permutation models]
  • A. Kripke–Platek set theory
    Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion 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. New Foundations for Mathematical Logic
    New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
  • 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. von Neumann paradox in set theory
    The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
  • 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: Fraenkel–Mostowski permutation models
Triple: [Abraham Fraenkel, knownFor, Fraenkel–Mostowski permutation models]
Generated description
Fraenkel–Mostowski permutation models are set-theoretic constructions using permutations of atoms to demonstrate the independence of certain choice principles from Zermelo–Fraenkel set theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fraenkel–Mostowski permutation models
Target entity description: Fraenkel–Mostowski permutation models are set-theoretic constructions using permutations of atoms to demonstrate the independence of certain choice principles from Zermelo–Fraenkel set theory.
  • A. Kripke–Platek set theory
    Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion 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. New Foundations for Mathematical Logic
    New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
  • 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. von Neumann paradox in set theory
    The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
  • 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.