Triple

T3913061
Position Surface form Disambiguated ID Type / Status
Subject axiom of choice E87367 entity
Predicate independentOf P243 FINISHED
Object Zermelo–Fraenkel set theory without 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 without choice | Statement: [axiom of choice, independentOf, Zermelo–Fraenkel set theory without choice]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Zermelo–Fraenkel set theory without choice
Context triple: [axiom of choice, independentOf, Zermelo–Fraenkel set theory without 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 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.
  • D. 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.
  • E. 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.
  • 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_69aed9424514819086e9c58adde6652d completed March 9, 2026, 2:29 p.m.
NER Named-entity recognition batch_69aeed37b19c81908e690c495d96607f completed March 9, 2026, 3:54 p.m.
NED1 Entity disambiguation (via context triple) batch_69b5285c52808190b9cbb2e3e03a18cb completed March 14, 2026, 9:20 a.m.
Created at: March 9, 2026, 3:22 p.m.