Triple

T9095778
Position Surface form Disambiguated ID Type / Status
Subject Ieke Moerdijk E218015 entity
Predicate notableWork P4 FINISHED
Object Algebraic Set Theory
Algebraic Set Theory is a branch of mathematical logic that develops set theory within a categorical and algebraic framework, often using topos theory and related structures.
 E777846 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: Algebraic Set Theory | Statement: [Ieke Moerdijk, notableWork, Algebraic Set Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Algebraic Set Theory
Context triple: [Ieke Moerdijk, notableWork, Algebraic Set Theory]
  • A. Lattice Theory
    Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
  • B. Universal Algebra
    Universal Algebra is a foundational mathematical text that systematically studies algebraic structures in a unified, abstract framework.
  • C. Grothendieck universe
    A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
  • 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. 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.
  • 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: Algebraic Set Theory
Triple: [Ieke Moerdijk, notableWork, Algebraic Set Theory]
Generated description
Algebraic Set Theory is a branch of mathematical logic that develops set theory within a categorical and algebraic framework, often using topos theory and related structures.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Algebraic Set Theory
Target entity description: Algebraic Set Theory is a branch of mathematical logic that develops set theory within a categorical and algebraic framework, often using topos theory and related structures.
  • A. Lattice Theory
    Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
  • B. Universal Algebra
    Universal Algebra is a foundational mathematical text that systematically studies algebraic structures in a unified, abstract framework.
  • C. Grothendieck universe
    A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
  • 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. 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.
  • 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_69ca83d9844081908e561e367fda6d45 completed March 30, 2026, 2:08 p.m.
NER Named-entity recognition batch_69cc96b650648190a8f59cee402d12aa completed April 1, 2026, 3:53 a.m.
NED1 Entity disambiguation (via context triple) batch_69d0180f70b88190a2d3dc49f32f0c2e completed April 3, 2026, 7:42 p.m.
NEDg Description generation batch_69d019652fe8819096cccb8cff431261 completed April 3, 2026, 7:47 p.m.
NED2 Entity disambiguation (via description) batch_69d01a290de881909482b7eb70bef0e3 completed April 3, 2026, 7:51 p.m.
Created at: March 30, 2026, 7:14 p.m.