Triple
T14265249
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Tarski–Mostowski–Robinson theorem |
E353626
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object |
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.
|
E1090230
|
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: Łoś–Tarski preservation theorem | Statement: [Tarski–Mostowski–Robinson theorem, isRelatedTo, Łoś–Tarski preservation theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Łoś–Tarski preservation theorem Context triple: [Tarski–Mostowski–Robinson theorem, isRelatedTo, Łoś–Tarski preservation theorem]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
- 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: Łoś–Tarski preservation theorem Triple: [Tarski–Mostowski–Robinson theorem, isRelatedTo, Łoś–Tarski preservation theorem]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Łoś–Tarski preservation theorem Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
- 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_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. |
| NEDg | Description generation | batch_69fd3417e8e88190b099bfe4ba30f364 |
completed | May 8, 2026, 12:53 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd37df3dfc8190a594abb2c14e11bb |
completed | May 8, 2026, 1:09 a.m. |
Created at: April 10, 2026, 1:09 a.m.