Recursive Functions and Intuitionistic Mathematics
E601583
Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Recursive Functions and Intuitionistic Mathematics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6594149 — 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: Recursive Functions and Intuitionistic Mathematics Context triple: [Stephen Kleene, notableWork, Recursive Functions and Intuitionistic Mathematics]
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A.
Elements of Intuitionism
Elements of Intuitionism is a foundational philosophical and logical treatise by Michael Dummett that systematically develops and defends intuitionistic logic and mathematics.
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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.
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C.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
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D.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
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E.
Kronecker’s finitism
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
- 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: Recursive Functions and Intuitionistic Mathematics Target entity description: Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
-
A.
Elements of Intuitionism
Elements of Intuitionism is a foundational philosophical and logical treatise by Michael Dummett that systematically develops and defends intuitionistic logic and mathematics.
-
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.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
-
D.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
-
E.
Kronecker’s finitism
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
logic textbook
ⓘ
mathematics book ⓘ |
| aim | to develop the theory of recursive functions within intuitionistic mathematics ⓘ |
| author |
Stephen C. Kleene
ⓘ
linked to:
Stephen Kleene
Stephen Cole Kleene ⓘ
linked to:
Stephen Kleene
|
| contribution |
formal treatment of constructive reasoning about recursive functions
ⓘ
integration of computability theory with intuitionistic logic ⓘ systematic development of recursion theory in an intuitionistic setting ⓘ |
| field |
constructive mathematics
ⓘ
intuitionistic mathematics ⓘ mathematical logic ⓘ recursion theory ⓘ |
| framework |
intuitionistic logic
ⓘ
intuitionistic mathematics ⓘ |
| hasConcept |
Turing computability
ⓘ
linked to:
Computability Theory
constructive existence proof ⓘ formal system for intuitionistic arithmetic ⓘ intuitionistic proof ⓘ lambda-definable function ⓘ partial recursive function ⓘ |
| influencedBy |
Alan Turing
ⓘ
Alonzo Church ⓘ Arend Heyting ⓘ Kurt Gödel ⓘ L. E. J. Brouwer ⓘ
linked to:
Luitzen Egbertus Jan Brouwer
|
| language | English ⓘ |
| notableFor |
being a seminal work in recursion theory
ⓘ
clarifying the role of recursive functions in intuitionistic frameworks ⓘ influencing later work in constructive and intuitionistic mathematics ⓘ |
| relatedTo |
Foundations of Intuitionistic Mathematics
ⓘ
Introduction to Metamathematics ⓘ Theory of recursive functions and effective computability ⓘ |
| subject |
Church–Turing thesis
ⓘ
arithmetical hierarchy ⓘ computable functions ⓘ constructive proof theory ⓘ formal systems ⓘ formalization of computation ⓘ intuitionistic logic ⓘ intuitionistic number theory ⓘ lambda-definability ⓘ partial recursive functions ⓘ primitive recursive functions ⓘ realizability ⓘ recursive functions ⓘ total recursive functions ⓘ |
| topic |
foundations of constructive arithmetic
ⓘ
relationship between computability and constructive 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.
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: Recursive Functions and Intuitionistic Mathematics Description of subject: Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.