Triple

T17871971
Position Surface form Disambiguated ID Type / Status
Subject Löwenheim–Skolem theorem E446857 entity
Predicate hasPart P35 FINISHED
Object upward Löwenheim–Skolem theorem — NE NERFINISHED

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: upward Löwenheim–Skolem theorem | Statement: [Löwenheim–Skolem theorem, hasPart, upward Löwenheim–Skolem theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: upward Löwenheim–Skolem theorem
Context triple: [Löwenheim–Skolem theorem, hasPart, upward Löwenheim–Skolem theorem]
  • A. Löwenheim–Skolem theorem (via additional arguments) chosen
    The Löwenheim–Skolem theorem is a fundamental result in model theory stating that any first-order theory with an infinite model has models of all infinite cardinalities, leading to the so-called Skolem paradox about the existence of countable models of set theory.
  • B. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • C. Vaught conjecture
    The Vaught conjecture is an open problem in mathematical logic and model theory that predicts a precise restriction on the possible numbers of countable models of a complete first-order theory.
  • D. Łoś–Tarski preservation theorem
    The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
  • E. Cantor’s theorem
    Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8b9f4c22c819093c2680434472894 completed April 10, 2026, 8:51 a.m.
NER Named-entity recognition batch_69e49aa30ff8819090c51c1d7767e952 completed April 19, 2026, 9:04 a.m.
Created at: April 10, 2026, 10:18 a.m.