Triple
T4492952
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | constructible universe |
E100621
|
entity |
| Predicate | hasReferenceWork |
P48731
|
FINISHED |
| Object |
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"
Gödel's 1940 monograph "The Consistency of the Continuum Hypothesis" is a landmark work in set theory that introduced the constructible universe (L) and proved that the Continuum Hypothesis and the Axiom of Choice are consistent with Zermelo–Fraenkel set theory, assuming ZF itself is consistent.
|
E446860
|
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: Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" | Statement: [constructible universe, hasReferenceWork, Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" Context triple: [constructible universe, hasReferenceWork, Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"]
-
A.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
-
B.
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik" is a foundational early 20th-century textbook that systematically developed first-order logic and helped establish mathematical logic as a rigorous formal discipline.
-
C.
Untersuchungen über die Grundlagen der Mengenlehre
Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
-
D.
New Foundations for Mathematical Logic
New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
-
E.
Gödel's ontological proof
Gödel's ontological proof is a formal, modal-logic-based argument for the existence of God that rigorously develops and refines earlier ontological arguments within a precise axiomatic framework.
- 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: Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" Triple: [constructible universe, hasReferenceWork, Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"]
Generated description
Gödel's 1940 monograph "The Consistency of the Continuum Hypothesis" is a landmark work in set theory that introduced the constructible universe (L) and proved that the Continuum Hypothesis and the Axiom of Choice are consistent with Zermelo–Fraenkel set theory, assuming ZF itself is consistent.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" Target entity description: Gödel's 1940 monograph "The Consistency of the Continuum Hypothesis" is a landmark work in set theory that introduced the constructible universe (L) and proved that the Continuum Hypothesis and the Axiom of Choice are consistent with Zermelo–Fraenkel set theory, assuming ZF itself is consistent.
-
A.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
-
B.
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik" is a foundational early 20th-century textbook that systematically developed first-order logic and helped establish mathematical logic as a rigorous formal discipline.
-
C.
Untersuchungen über die Grundlagen der Mengenlehre
Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
-
D.
New Foundations for Mathematical Logic
New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
-
E.
Gödel's ontological proof
Gödel's ontological proof is a formal, modal-logic-based argument for the existence of God that rigorously develops and refines earlier ontological arguments within a precise axiomatic framework.
- 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_69bd43cdf15081909a4fa2585ff63b3e |
completed | March 20, 2026, 12:55 p.m. |
| NER | Named-entity recognition | batch_69bd5570ba0881908f5fb4f8d0730e64 |
completed | March 20, 2026, 2:10 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bd67b40fd4819098636b6f29304312 |
completed | March 20, 2026, 3:28 p.m. |
| NEDg | Description generation | batch_69bd688e84fc8190a8900be40e3cf694 |
completed | March 20, 2026, 3:32 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bd69bcf10c8190bd6ceb6bc604b3f5 |
completed | March 20, 2026, 3:37 p.m. |
Created at: March 20, 2026, 12:59 p.m.