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: Recursion theorem | Statement: [Rice's theorem, relatedTo, Recursion theorem]

Target entity: Recursion theorem
Context triple: [Rice's theorem, relatedTo, Recursion theorem]

• A. Kleene’s recursion theorem chosen
  Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
• B. Rice's theorem
  Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
• C. Löb's theorem
  Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
• D. Kleene’s normal form theorem
  Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
• E. Tarski's undefinability theorem
  Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.