Triple

T4493079
Position Surface form Disambiguated ID Type / Status
Subject Paul Cohen E100624 entity
Predicate notableConcept P201 FINISHED
Object forcing (set theory)
Forcing (set theory) is a powerful technique in mathematical logic, introduced by Paul Cohen, used to construct models of set theory and prove the independence of certain propositions from Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC).
E446865 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: forcing (set theory) | Statement: [Paul Cohen, notableConcept, forcing (set theory)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: forcing (set theory)
Context triple: [Paul Cohen, notableConcept, forcing (set theory)]
  • A. 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.
  • B. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
  • C. 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.
  • D. constructible universe
    The constructible universe is a class model of set theory introduced by Kurt Gödel that systematically builds sets in hierarchical stages and shows the relative consistency of the axiom of choice and the generalized continuum hypothesis with ZF.
  • E. 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.
  • 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: forcing (set theory)
Triple: [Paul Cohen, notableConcept, forcing (set theory)]
Generated description
Forcing (set theory) is a powerful technique in mathematical logic, introduced by Paul Cohen, used to construct models of set theory and prove the independence of certain propositions from Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC).
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: forcing (set theory)
Target entity description: Forcing (set theory) is a powerful technique in mathematical logic, introduced by Paul Cohen, used to construct models of set theory and prove the independence of certain propositions from Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC).
  • A. 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.
  • B. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
  • C. 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.
  • D. constructible universe
    The constructible universe is a class model of set theory introduced by Kurt Gödel that systematically builds sets in hierarchical stages and shows the relative consistency of the axiom of choice and the generalized continuum hypothesis with ZF.
  • E. 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.
  • 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_69bd43cdf15081909a4fa2585ff63b3e completed March 20, 2026, 12:55 p.m.
NER Named-entity recognition batch_69bd5570ba0881908f5fb4f8d0730e64 completed March 20, 2026, 2:10 p.m.
NED1 Entity disambiguation (via context triple) batch_69bd67b40fd4819098636b6f29304312 completed March 20, 2026, 3:28 p.m.
NEDg Description generation batch_69bd688e84fc8190a8900be40e3cf694 completed March 20, 2026, 3:32 p.m.
NED2 Entity disambiguation (via description) batch_69bd69bcf10c8190bd6ceb6bc604b3f5 completed March 20, 2026, 3:37 p.m.
Created at: March 20, 2026, 12:59 p.m.