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: Gödel's first incompleteness theorem | Statement: [Löb's theorem, relatedTo, Gödel's first incompleteness theorem]

Target entity: Gödel's first incompleteness theorem
Context triple: [Löb's theorem, relatedTo, Gödel's first incompleteness theorem]

• A. Gödel's incompleteness theorems chosen
  Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
• B. 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.
• 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. Reflections on Kurt Gödel
  Reflections on Kurt Gödel is a philosophical and biographical study in which logician Hao Wang presents his conversations with and insights about Kurt Gödel’s life, work, and views on logic, mathematics, and philosophy.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.