Triple

T3390172
Position Surface form Disambiguated ID Type / Status
Subject Gödel's incompleteness theorems E71396 entity
Predicate appliesTo P1129 FINISHED
Object Zermelo–Fraenkel set theory with Choice 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 with Choice | Statement: [Gödel's incompleteness theorems, appliesTo, Zermelo–Fraenkel set theory with Choice]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Zermelo–Fraenkel set theory with Choice
Context triple: [Gödel's incompleteness theorems, appliesTo, Zermelo–Fraenkel set theory with Choice]
  • 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. Untersuchungen über die Grundlagen der Mengenlehre
    Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
  • 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_69ad85a9c4a88190a854019341cb3b60 completed March 8, 2026, 2:20 p.m.
NER Named-entity recognition batch_69adb6682c708190b76a7a16cee7c5aa completed March 8, 2026, 5:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69b3345a95ac819098be25233b8e0ed5 completed March 12, 2026, 9:47 p.m.
Created at: March 8, 2026, 3:14 p.m.