Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Heyting arithmetic | Statement: [Arend Heyting, notableFor, Heyting arithmetic]

Target entity: Heyting arithmetic
Context triple: [Arend Heyting, notableFor, Heyting 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
• G. Unsure - the case is ambiguous/there is not enough information to decide.

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