Triple

T3690404
Position Surface form Disambiguated ID Type / Status
Subject Cantor’s theorem E78328 entity
Predicate holdsIn P17841 FINISHED
Object Zermelo–Fraenkel set theory E13857 NE FINISHED

How this triple was built (2 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: Zermelo–Fraenkel set theory | Statement: [Cantor’s theorem, holdsIn, Zermelo–Fraenkel set theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Zermelo–Fraenkel set theory
Context triple: [Cantor’s theorem, holdsIn, Zermelo–Fraenkel set theory]
  • A. Zermelo–Fraenkel set theory chosen
    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.
  • 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. von Neumann–Bernays–Gödel set theory
    Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
  • D. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ad85e285a081908f8cbfa9e2ed9b75 completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adc4e6147c8190ae358e8cc94f479c completed March 8, 2026, 6:50 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4c3c9e9c08190bd97642ccf39b172 completed March 14, 2026, 2:11 a.m.
Created at: March 8, 2026, 3:26 p.m.