Heyting arithmetic
E1343172
UNEXPLORED
Heyting arithmetic is a formal system of arithmetic based on intuitionistic logic, serving as the constructive counterpart to classical Peano arithmetic.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Heyting arithmetic canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T18793327 — 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: Heyting arithmetic Context triple: [Arend Heyting, notableFor, Heyting arithmetic]
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A.
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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B.
Recursive Functions and Intuitionistic Mathematics
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.
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C.
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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D.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
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E.
Gentzen’s consistency proof for arithmetic
Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
- 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: Heyting arithmetic Target entity description: Heyting arithmetic is a formal system of arithmetic based on intuitionistic logic, serving as the constructive counterpart to classical Peano arithmetic.
-
A.
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.
-
B.
Recursive Functions and Intuitionistic Mathematics
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.
-
C.
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.
-
D.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
-
E.
Gentzen’s consistency proof for arithmetic
Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.