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: undecidability theorem | Statement: [Rice's theorem, typeOf, undecidability theorem]

Target entity: undecidability theorem
Context triple: [Rice's theorem, typeOf, undecidability theorem]

• A. Rice's theorem chosen
  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.
• 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. Gödel's incompleteness theorems
  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.
• D. Halting problem
  The halting problem is a fundamental decision problem in computability theory that asks whether a given program will eventually stop running or continue to run forever, and is famously proven to be undecidable.
• E. Entscheidungsproblem
  The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.