Triple

T14265289
Position Surface form Disambiguated ID Type / Status
Subject Tarski’s theorem on the completeness of elementary algebra and geometry E353627 entity
Predicate relatedTo P37 FINISHED
Object Tarski–Seidenberg theorem E353634 NE FINISHED

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: Tarski–Seidenberg theorem | Statement: [Tarski’s theorem on the completeness of elementary algebra and geometry, relatedTo, Tarski–Seidenberg theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Tarski–Seidenberg theorem
Context triple: [Tarski’s theorem on the completeness of elementary algebra and geometry, relatedTo, Tarski–Seidenberg theorem]
  • A. Positivstellensatz
    The Positivstellensatz is a fundamental result in real algebraic geometry that characterizes when a polynomial that is positive on a semialgebraic set can be represented using sums of squares and polynomial inequalities.
  • B. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • C. “A Decision Method for Elementary Algebra and Geometry” chosen
    “A Decision Method for Elementary Algebra and Geometry” is Alfred Tarski’s influential work that presents a procedure for deciding the truth of statements in elementary algebra and geometry, laying foundations for decision theory in mathematical logic.
  • D. 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.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de6357a8188190ba518a486521052b completed April 14, 2026, 3:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd326551b08190ae8fe220a6422339 completed May 8, 2026, 12:46 a.m.
Created at: April 10, 2026, 1:09 a.m.