Triple

T10462279
Position Surface form Disambiguated ID Type / Status
Subject Thoralf Skolem E246704 entity
Predicate notableWork P4 FINISHED
Object Skolem arithmetic
Skolem arithmetic is a fragment of first-order arithmetic focusing on the natural numbers with multiplication but without addition, studied for its distinctive decidability and model-theoretic properties.
E865123 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: Skolem arithmetic | Statement: [Thoralf Skolem, notableWork, Skolem arithmetic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Skolem arithmetic
Context triple: [Thoralf Skolem, notableWork, Skolem arithmetic]
  • A. Peano arithmetic
    Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number 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. Skolemization
    Skolemization is a logical transformation technique that eliminates existential quantifiers by introducing Skolem functions or constants, commonly used in automated theorem proving and first-order logic.
  • D. Herbrand's theorem
    Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
  • E. Tarski’s theorem on the completeness of elementary algebra and geometry
    Tarski’s theorem on the completeness of elementary algebra and geometry is a foundational result in mathematical logic showing that the first-order theory of real closed fields (capturing elementary algebra and Euclidean geometry) is complete, decidable, and admits quantifier elimination.
  • 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: Skolem arithmetic
Triple: [Thoralf Skolem, notableWork, Skolem arithmetic]
Generated description
Skolem arithmetic is a fragment of first-order arithmetic focusing on the natural numbers with multiplication but without addition, studied for its distinctive decidability and model-theoretic properties.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Skolem arithmetic
Target entity description: Skolem arithmetic is a fragment of first-order arithmetic focusing on the natural numbers with multiplication but without addition, studied for its distinctive decidability and model-theoretic properties.
  • A. Peano arithmetic
    Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number 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. Skolemization
    Skolemization is a logical transformation technique that eliminates existential quantifiers by introducing Skolem functions or constants, commonly used in automated theorem proving and first-order logic.
  • D. Herbrand's theorem
    Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
  • E. Tarski’s theorem on the completeness of elementary algebra and geometry
    Tarski’s theorem on the completeness of elementary algebra and geometry is a foundational result in mathematical logic showing that the first-order theory of real closed fields (capturing elementary algebra and Euclidean geometry) is complete, decidable, and admits quantifier elimination.
  • 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_69d381c16c248190a2fe5b471e584e9c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d50884fac48190af22e181b1492557 completed April 7, 2026, 1:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69d89fcc84b48190a39de0d9b9111ebd completed April 10, 2026, 6:59 a.m.
NEDg Description generation batch_69d8a1656b348190ba932d03402d6a4d completed April 10, 2026, 7:06 a.m.
NED2 Entity disambiguation (via description) batch_69d8a2b82bb48190899f37a967fef444 completed April 10, 2026, 7:11 a.m.
Created at: April 6, 2026, 12:19 p.m.