Introduction to Metamathematics
E601582
Introduction to Metamathematics is a classic 1952 textbook by Stephen Kleene that systematically develops the foundations of mathematical logic and recursion theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Introduction to Metamathematics canonical | 2 |
| Kleene’s book "Introduction to Metamathematics" | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6594148 — 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: Introduction to Metamathematics Context triple: [Stephen Kleene, notableWork, Introduction to Metamathematics]
-
A.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
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B.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
C.
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 is a landmark anthology that collects and translates many of the foundational papers in modern mathematical logic from the late 19th to early 20th century.
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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.
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E.
“Logic, Semantics, Metamathematics”
“Logic, Semantics, Metamathematics” is a landmark collection of Alfred Tarski’s foundational papers that helped shape modern logic, model theory, and the formal study of truth.
- 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: Introduction to Metamathematics Target entity description: Introduction to Metamathematics is a classic 1952 textbook by Stephen Kleene that systematically develops the foundations of mathematical logic and recursion theory.
-
A.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
-
B.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
C.
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 is a landmark anthology that collects and translates many of the foundational papers in modern mathematical logic from the late 19th to early 20th century.
-
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.
“Logic, Semantics, Metamathematics”
“Logic, Semantics, Metamathematics” is a landmark collection of Alfred Tarski’s foundational papers that helped shape modern logic, model theory, and the formal study of truth.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
textbook ⓘ |
| author |
Stephen Cole Kleene
ⓘ
linked to:
Stephen Kleene
Stephen Kleene ⓘ |
| countryOfOrigin |
United States
ⓘ
linked to:
United States of America
|
| describedAs |
classic text in mathematical logic
ⓘ
standard reference in recursion theory ⓘ |
| emphasizes | rigorous metatheoretic proofs ⓘ |
| field |
mathematical logic
ⓘ
recursion theory ⓘ |
| genre |
logic textbook
ⓘ
mathematics textbook ⓘ |
| hasPart |
chapter on formal number theory
ⓘ
chapter on incompleteness ⓘ chapter on predicate calculus ⓘ chapter on propositional calculus ⓘ chapter on recursive functions ⓘ chapter on undecidability ⓘ |
| influenced |
development of recursion theory
ⓘ
teaching of mathematical logic ⓘ |
| intendedAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ logicians ⓘ |
| language | English ⓘ |
| notableFor |
detailed treatment of Gödel numbering
ⓘ
early comprehensive exposition of incompleteness results ⓘ systematic development of recursion theory ⓘ |
| publicationYear | 1952 ⓘ |
| publisher |
North-Holland
ⓘ
Van Nostrand ⓘ |
| topic |
Gödel incompleteness theorems
ⓘ
linked to:
Gödel's incompleteness theorems
arithmetization of syntax ⓘ completeness theorems ⓘ computability theory ⓘ consistency proofs ⓘ decision problems ⓘ first-order logic ⓘ formal arithmetic ⓘ formal systems ⓘ foundations of mathematics ⓘ models and interpretations ⓘ proof theory ⓘ propositional logic ⓘ recursive functions ⓘ |
| usesFramework | formal axiomatic method ⓘ |
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.
Instruction
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.
Input
Subject: Introduction to Metamathematics Description of subject: Introduction to Metamathematics is a classic 1952 textbook by Stephen Kleene that systematically develops the foundations of mathematical logic and recursion theory.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Introduction to Metamathematics