“A Decision Method for Elementary Algebra and Geometry”
E353634
“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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Tarski–Seidenberg theorem | 1 |
| Tarski’s high school algebra problem | 1 |
| “A Decision Method for Elementary Algebra and Geometry” canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3380955 — 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.
Target entity: “A Decision Method for Elementary Algebra and Geometry” Context triple: [Alfred Tarski, notableWork, “A Decision Method for Elementary Algebra and Geometry”]
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A.
"The Complexity of Theorem-Proving Procedures"
"The Complexity of Theorem-Proving Procedures" is Stephen Cook’s landmark 1971 paper that introduced the concept of NP-completeness and proved the Boolean satisfiability problem (SAT) to be NP-complete, laying the foundation for modern computational complexity theory.
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B.
Handbook of Automated Reasoning
The "Handbook of Automated Reasoning" is a comprehensive reference work that surveys the theories, methods, and tools used in the field of automated theorem proving and formal reasoning in computer science and logic.
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C.
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.
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D.
Recherches sur la théorie de la démonstration
Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
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E.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: “A Decision Method for Elementary Algebra and Geometry” Target entity description: “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.
-
A.
"The Complexity of Theorem-Proving Procedures"
"The Complexity of Theorem-Proving Procedures" is Stephen Cook’s landmark 1971 paper that introduced the concept of NP-completeness and proved the Boolean satisfiability problem (SAT) to be NP-complete, laying the foundation for modern computational complexity theory.
-
B.
Handbook of Automated Reasoning
The "Handbook of Automated Reasoning" is a comprehensive reference work that surveys the theories, methods, and tools used in the field of automated theorem proving and formal reasoning in computer science and logic.
-
C.
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.
-
D.
Recherches sur la théorie de la démonstration
Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
-
E.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ work in mathematical logic ⓘ |
| author | Alfred Tarski ⓘ |
| basedOn | quantifier elimination for real-closed fields ⓘ |
| contribution |
lays foundations for decision theory in mathematical logic
ⓘ
presents a decision method for elementary algebra ⓘ presents a decision method for elementary geometry ⓘ provides an algorithmic procedure to decide truth of certain mathematical statements ⓘ shows decidability of the first-order theory of real-closed fields ⓘ |
| describes |
procedure for deciding truth of statements in elementary algebra
ⓘ
procedure for deciding truth of statements in elementary geometry ⓘ |
| field |
algebra
ⓘ
decision theory in logic ⓘ geometry ⓘ mathematical logic ⓘ model theory ⓘ |
| hasNotableAuthor | Alfred Tarski ⓘ |
| influenced |
automated theorem proving
ⓘ
computer algebra systems ⓘ development of decision procedures in logic ⓘ |
| influencedBy |
first-order logic
ⓘ
real algebraic geometry ⓘ |
| language | English ⓘ |
| mainTopic |
decision procedures
ⓘ
elementary algebra ⓘ elementary geometry ⓘ first-order theory of real-closed fields ⓘ |
| notableFor |
being an early systematic treatment of decision methods in logic
ⓘ
showing that many problems in algebra and geometry are algorithmically decidable ⓘ |
| relatedTo |
Tarski–Seidenberg theorem
ⓘ
decidability of real-closed fields ⓘ |
| topic |
algorithmic decidability
ⓘ
elimination of quantifiers ⓘ formalization of algebra and geometry in first-order logic ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Subject: “A Decision Method for Elementary Algebra and Geometry” Description of subject: “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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.