Triple

T17872099
Position Surface form Disambiguated ID Type / Status
Subject model theory E446859 entity
Predicate hasKeyConcept P533 FINISHED
Object 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: Löwenheim–Skolem theorem | Statement: [model theory, hasKeyConcept, Löwenheim–Skolem theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Löwenheim–Skolem theorem
Context triple: [model theory, hasKeyConcept, 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. Tarski's undefinability theorem
    Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
  • 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. compactness theorem
    The compactness theorem is a fundamental result in mathematical logic stating that a set of first-order sentences has a model if and only if every finite subset of it has a model.
  • 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_69e49aa3cd248190a13a8209ba44fd3b completed April 19, 2026, 9:04 a.m.
Created at: April 10, 2026, 10:18 a.m.