Hilbert's axioms
E1328311
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Hilbert's axioms are a rigorous, foundational set of logical assumptions introduced by David Hilbert to provide a complete and consistent basis for Euclidean geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hilbert's axioms canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T18491561 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hilbert's axioms Context triple: [Euclidean geometry, formalizedBy, Hilbert's axioms]
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A.
Euclid's postulates
Euclid's postulates are the foundational axioms of classical Euclidean geometry, defining basic properties of points, lines, and planes from which the rest of the geometry is logically derived.
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B.
The Foundations of Geometry
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
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C.
Playfair's axiom
Playfair's axiom is a reformulation of Euclid’s parallel postulate stating that through a point not on a given line there is exactly one line parallel to the given line, fundamental to Euclidean geometry.
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D.
Veblen axioms for projective geometry
The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
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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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hilbert's axioms Target entity description: Hilbert's axioms are a rigorous, foundational set of logical assumptions introduced by David Hilbert to provide a complete and consistent basis for Euclidean geometry.
-
A.
Euclid's postulates
Euclid's postulates are the foundational axioms of classical Euclidean geometry, defining basic properties of points, lines, and planes from which the rest of the geometry is logically derived.
-
B.
The Foundations of Geometry
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
-
C.
Playfair's axiom
Playfair's axiom is a reformulation of Euclid’s parallel postulate stating that through a point not on a given line there is exactly one line parallel to the given line, fundamental to Euclidean geometry.
-
D.
Veblen axioms for projective geometry
The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
-
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
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.